Methods for reconstructing an unknown object in a scanned image

ABSTRACT

A method for assigning attributes to an unknown object includes the steps of scanning the unknown object at least partially overlapping with a background object within an x-ray scanning device to provide dual-energy attenuation images having dual-energy attenuation information representing an overlap region wherein the background object and the unknown object overlap, decomposing the attenuation images into reference material equivalent path length images, removing the background object to provide reference material equivalent path lengths representing the unknown object, converting the reference material equivalent path lengths representing the unknown object into unknown object path lengths multiplied by a predetermined scaling factor, reducing the scaling factor to provide a contour of the unknown object and unknown object path lengths, and, determining a density and effective atomic number of the unknown object.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a non-provisional of and claims priority toand the benefit of U.S. Provisional Patent Application No. 62/615,120,filed on Jan. 9, 2018, entitled “METHODS AND APPARATUS FOR DETERMININGAND ANALYZING THE PROPERTIES OF AN OBJECT SCANNED WITH IONIZINGELECTROMAGNETIC RADIATION”, which is incorporated by reference in itsentirety.

BACKGROUND

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

There are presently many methods and apparatus for scanning objects andmaterials using electromagnetic radiation, such as x-rays, for thepurpose of identifying the material of which the object being scanned ismade. Although certain techniques are useful in basic medical imagingapplications, such techniques usually do not provide a continuousdiscrimination of materials over a wide range of atomic compositionrequired for identifying materials for security screening, whichinvolves identifying materials which may pose a threat. Moreover,security screening of objects is often used at locations with highthroughput, such as airports, where people and baggage must be scannedat a relatively high rate so as to avoid congestion at securitycheckpoints.

Liquid, aerosol or gel (LAG) materials are of particular concern becausethey can be stored in small containers that are often carried bypassengers, such as drinking bottles, and may potentially be composed ofan explosive material. Moreover, non-explosive LAG materials,particularly liquids, may be stored in separate containers and maypotentially be later combined to make a material which is explosive. Thevolume of potentially explosive LAG material stored in small containersmay be sufficient to damage an aircraft or pose a serious safety risk topassengers nearby in an aircraft or in an airport. Proper identificationof LAG materials and their properties during screening operations istherefore important.

In some systems, an object is scanned and an image of the scanned objectis generated for review by human operator such as security personnel atan airport. In other systems, software may be used for the purpose ofprocessing a generated or refined image to identify potentiallythreatening, smuggled or illicit objects or materials. The softwaredetermines whether the pixels of the image represent an object ormaterial of interest and the image may then be forwarded to a humanoperator for second-level screening. In such cases, there is introduceda “human intervention” step and therefore a step whereby human error maybe introduced. For example, a human operator reviewing the image mayfail to identify potentially threatening materials or objects containedin the image. There is also introduced a problem of limited throughputat security stations due to the time required for security personnel toreview the image flagged by the software, as well as the decision-makingprocess for possible rerouting of personnel, baggage and/or passengers.Such human intervention may cause undue delay at the security screeningcheckpoint or may come at prohibitive cost. Moreover, while securitypersonnel review the information provided in the refined image, theirattention is diverted away from their surroundings and therefore awayfrom potentially threatening situations.

Some systems have been put in place to manage passenger throughput atairport security screening checkpoints. However, the reliance on refinedimage data and processing by human operators does not efficientlyaddress the complications associated with steady throughput at securityscreening checkpoints.

In view of the above, advantage would be found with an apparatus andmethod which facilitates automatic analysis of x-ray screeninginformation to limit or eliminate potential for human error and toprocess this information in real time or near real time and preferablyautomatically so as to maintain efficient throughput at locations wherescanning may be performed.

SUMMARY

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

In a first aspect, there is provided a method for assigning attributesto an unknown object including the steps of scanning the unknown objectwithin a container and at least partially overlapping with a backgroundobject within an x-ray scanning device. The x-ray scanning device emitsx-rays from at least two sources which pass through the object ofinterest and the background object. The x-rays are detected by at leastone array of detectors to provide a plurality of dual-energy attenuationimages each having dual-energy attenuation information representing thecontainer and an overlap region wherein the background object and theunknown object and container overlap. The method further includes thesteps of decomposing each of the dual-energy attenuation images intoreference material equivalent path length images, removing the referencematerial equivalent path lengths representing the background object fromthe reference material equivalent path length images to providereference material equivalent path lengths representing the unknownobject and the container, converting the reference material equivalentpath lengths representing the unknown object into unknown object pathlengths multiplied by a predetermined scaling factor, determining theeffective atomic number for each pixel representing the unknown objectand the container, determining the mass thickness for each pixelrepresenting the unknown object and the container, the mass thicknessbeing equivalent to the unknown object path lengths multiplied by thescaling factor, identifying each first source-detector pair line definedby a first x-ray extending between a first one of the at least twosources and one detector of the array of detectors in a first one of theplurality of dual-energy attenuation images on which lies one scaledunknown object path length, identifying each second source-detector pairline defined by a second x-ray extending between a second one of the atleast two sources and one detector of the array of detectors in a secondone of the plurality of dual-energy attenuation images on which lies oneother scaled unknown object path length, the second one of the pluralityof dual-energy attenuation images generated contemporaneously with thefirst one of the plurality of dual-energy attenuation images, joiningthe extremities of each of the scaled unknown object path lengths toprovide a contour of the unknown object, iteratively matching thecontour of the unknown object of each of the first and the second one ofthe plurality of dual-energy attenuation images to reduce the scalingfactor of the scaled unknown object path lengths and to provide unknownobject path lengths, defining the contour of the unknown object as aninner contour of the container, identifying third source-detector pairlines defined by third x-rays extending between each source and onedetector of the array which intersect with the container at only onepoint of intersection in each of the first and second one of theplurality of dual-energy attenuation images and delimit an outer boundof the container as the pixels within the third source-detector lines,interpolating the outer bound of the container extending between the onepoint of intersection of each third source-detector pair line to definean outer contour of the container, determining path lengths representingthe container as path lengths which extend between the inner contour ofthe container and the outer contour of the container, and, determining adensity of the unknown object and an effective atomic number of theunknown object.

In one aspect, the step of decomposing the plurality of dual-energyattenuation images into reference material equivalent path length imagesfurther includes the steps of retrieving from lookup tables saveddual-reference material equivalent path lengths associated with thedual-energy x-ray attenuation information corresponding with thedual-energy attenuation images.

In another aspect, the step of decomposing the plurality of dual-energyattenuation images into reference material equivalent path length imagesmay further include the steps of scanning in the x-ray scanning device,first and second reference materials each having known atomiccomposition, known dimensions and known orientation in the x-rayscanning device, the x-ray scanning device emitting x-rays which passthrough the first reference material with first reference material pathlengths and through the second reference material with second referencematerial path lengths to provide dual-energy x-ray attenuationinformation, associating the dual-energy x-ray attenuation informationfor each pixel in the dual-energy attenuation images with each of thefirst reference material path lengths and the second reference materialpath lengths, expressing collectively each of the first referencematerial equivalent path lengths and the second reference materialequivalent path lengths as a function of the associated dual-energyx-ray attenuation information to define dual-energy attenuationsurfaces, and, imposing dual-energy attenuation information of thedual-energy attenuation images onto the dual-energy attenuation surfacesto determine corresponding first reference material equivalent pathlengths and second reference material equivalent path lengthscorresponding with the dual-energy attenuation information.

The dual-energy attenuation images may include low-energy attenuationimages and high-energy attenuation images, the dual-reference materialequivalent path length images may include first reference materialequivalent path length images and second reference material equivalentpath length images and the dual-energy x-ray attenuation information mayinclude high-energy x-ray attenuation information and low-energy x-rayattenuation information.

The expressing step may further include the step of invertingnumerically point-by-point the dual-energy attenuation surfaces using anoptimization algorithm to provide inverse dual-energy attenuationsurfaces.

The expressing step may further include the steps of selecting a modelfor expressing collectively each of the first reference materialequivalent path lengths and the second reference material equivalentpath lengths as a function of the associated dual-energy x-rayattenuation information to define dual-energy attenuation surfaces.

The step of selecting the model may further includes the steps ofselecting a set of coefficients to be applied to the model for fittingthe dual-energy x-ray attenuation information with the model, and,fitting the dual-energy x-ray attenuation information with the model byoptimizing the coefficients.

The step of selecting the model may further include the steps ofselecting the set of fitting constraints to be applied to the model forselecting the coefficients, and, selecting the set of coefficients byapplying the set of fitting constraints to the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation, and the associating step may further include defining afirst space wherein the low-energy x-ray attenuation information of thefirst reference material and the second reference material defines afirst plane and first reference material equivalent path lengths andsecond reference material equivalent path lengths each define a firstheight over the first plane, defining a second space wherein thehigh-energy x-ray attenuation information of the first referencematerial and the second reference material defines a second plane andfirst reference material equivalent path lengths and second referencematerial equivalent path lengths each define a second height over secondthe plane, and, representing collectively the first reference materialequivalent path lengths and the second reference material equivalentpath lengths using the model to define the dual-energy attenuationsurfaces.

In another aspect, the model is a second model, the dual-energyattenuation surfaces are inverse attenuation surfaces, and prior to theassociating step, the method further includes the steps of associatingeach of the dual-energy x-ray attenuation information with correspondingones of each of the first reference material equivalent path lengths andthe second reference material equivalent path lengths, and, selecting afirst model for expressing collectively the dual-energy x-rayattenuation information as a function of the first reference materialequivalent path lengths and the second reference material equivalentpath lengths to define direct attenuation surfaces.

The step of selecting the first model may further include the steps ofselecting a first set of coefficients to be applied to the first modelfor fitting the dual-energy x-ray attenuation information with the firstmodel, and, fitting the dual-energy x-ray attenuation information withthe first model by optimizing the first coefficients. The step ofselecting the second model further includes the steps of selecting asecond set of coefficients to be applied to the second model for fittingthe dual-energy x-ray attenuation information with the second model,and, fitting the dual-energy x-ray attenuation information with thesecond model optimizing the second set of coefficients.

The step of selecting the first model may further include the steps ofselecting a first set of fitting constraints to be applied to the firstmodel for selecting the first set of coefficients, and, selecting theset of first coefficients by applying the first set of fittingconstraints to the first model. The step of selecting second the modelfurther includes the steps of selecting a second set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients, and, selecting the second set of coefficients byapplying the second set of fitting constraints to the second model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the associating step may further include the steps ofdefining a space wherein the first reference material equivalent pathlengths and the second reference material equivalent path lengths definea first plane and the high-energy x-ray attenuation information and thelow-energy x-ray attenuation information each define a respective firstand second height over the first plane and represent collectively thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information using the first model to define the directattenuation surfaces, and, defining an inverse space wherein thelow-energy x-ray attenuation information and the high-energy x-rayattenuation information define a second plane and first referencematerial equivalent path lengths and second reference materialequivalent path lengths each define a respective third and fourth heightover the second plane and representing collectively the first referencematerial equivalent path lengths and the second reference materialequivalent path lengths using the second model to define the inverseattenuation surfaces.

The method may further include the steps of determining the mass densityof each of the first and second reference materials, determining aproduct of the first reference material equivalent path lengths and themass density of the first reference material to provide a firstreference material mass thickness, determining a product of the secondreference material equivalent path lengths and the mass density of thesecond reference material to provide a second reference material massthickness, and, determining a total reference material mass thickness bysumming the first reference material mass thickness and the secondreference material mass thickness.

The dual-energy x-ray attenuation information may further includeshigh-energy x-ray attenuation information and low-energy x-rayattenuation information, and the step of decomposing each of thedual-energy attenuation images into reference material equivalent pathlength images may further comprise the steps of, for each of the firstand second reference materials, determining an energy-dependentattenuation cross section based on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation, defining a Z_(eff)-dependent cross-section wherein aZ_(eff) value is dependent on each of the high-energy x-ray attenuationinformation and the low-energy x-ray attenuation information, evaluatingan energy-dependent material transmittance function using each of theenergy-dependent attenuation cross sections, re-evaluating theenergy-dependent material transmittance function using each of theZ_(eff)-dependent cross-sections to provide a high-energy level domainZ_(eff)-dependent material transmittance function, a high-energy leveldomain weighted squared transmission error, a low-energy level domainZ_(eff)-dependent material transmittance function, and a low-energylevel domain weighted squared transmission error, and, minimizing thelow-energy level domain weighted squared transmission error to assign aZ_(eff) value to each of the first and second reference materials.

The step of determining the energy-dependent attenuation cross sectionbased on each of the low-energy x-ray attenuation information and thehigh-energy x-ray attenuation information may further include the stepof, for each of the first and second reference materials, determiningone of an average, a median and a mean of energy-dependent attenuationcross-sections per mol of electron of each element in the referencematerial, weighted by the total number of electrons of each element inthe reference material.

The step of determining the one of the average, the median and the meanof energy-dependent attenuation cross-section per mol of electron ofeach element in the reference material may further include the steps of,for each of the first and second reference material, determining theproduct of a known mass attenuation coefficient of the referencematerial and a molar mass over the number of electrons per unionizedatom of each element in the reference material.

The step of defining Z_(eff)-dependent cross-section may further includethe step of, for each of the first and second reference materials,determining a linear combination of energy-dependent attenuationcross-sections of each of the two elements having atomic numbersimmediately adjacent to the effective atomic number value on which theZ_(eff)-dependent cross-section is based.

The step of evaluating an energy-dependent material transmittancefunction may further include, for each of the first and second referencematerials, evaluating an inverse exponential function of an electrondensity of the reference material and the energy-dependent attenuationcross-section of the reference material.

The step of minimizing the low-energy level domain weighted squaredtransmission error may further include the step of, for each of thefirst and second reference materials, integrating a weighted differencebetween the energy-dependent material transmittance function and thecorresponding Z_(eff)-dependent material transmittance function.

The step of converting the reference material equivalent path lengthsrepresenting the unknown object into unknown object path lengthsmultiplied by a predetermined scaling factor may further include thestep of applying the following function for each of the first and secondreference material equivalent path lengths representing the unknownobject:

${t_{o}\left( {i,j} \right)} = {\frac{\rho \; {t_{ob}\left( {i,j} \right)}}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}$$\begin{matrix}{{t_{o}^{*}\left( {i,j} \right)} = {\rho \; {t_{ob}\left( {i,j} \right)}\left( {{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right) \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {SF}}}\end{matrix}$${{With}\mspace{14mu} {SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}\mspace{14mu} {when}\mspace{14mu} {t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}$

wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants.

The dual-energy attenuation information may include high-energyattenuation information and low-energy attenuation information and thestep of determining the effective atomic number of the unknown objectmay further include the steps of determining a first weight fraction ofeach of the first and second reference materials in the unknown object,determining a second weight fraction of each element of each of thefirst and second reference materials in the unknown object, determininga mass attenuation coefficient of the unknown object, determine anenergy-dependent attenuation cross section of the unknown object,defining a Z_(eff)-dependent cross-section of the unknown object whereina Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation, evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections,re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror, and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to the unknown object.

The step of determining the mass attenuation coefficient for the unknownobject may further include the steps of determining an effective weightfraction of each element of each reference material in the unknownmaterial, determining a mass attenuation coefficient of each element ofeach reference material in the unknown material, and, determining aproduct of the effective weight fraction and mass attenuationcoefficient of each element of each reference material in the unknownmaterial.

In one aspect, the background object is a predetermined backgroundobject, and the step of removing the reference material equivalent pathlengths representing the background object from the reference materialequivalent path length images may further include the steps of, scanningthe predetermined background object in a plurality of positions andorientations within an x-ray scanning device to obtain a plurality ofpredetermined background object dual-energy attenuation images eachhaving predetermined background object dual-energy attenuationinformation representing the predetermined background object,decomposing the predetermined background object dual-energy attenuationimages into predetermined background object dual-reference materialequivalent path length images having predetermined background objectreference material equivalent path lengths passing through thepredetermined background object, determining the position andorientation of the background object in one of the background objectdual-energy attenuation images and the dual-reference materialequivalent path length images of the unknown object by using asegmentation algorithm to localize the background object, determining,by comparison, corresponding ones of the plurality of predeterminedbackground object reference material equivalent path length images whichmost closely corresponds with the position and orientation of thebackground object in the dual-reference material equivalent path lengthimages, and, eliminating the predetermined background object referencematerial equivalent path lengths of the corresponding ones of theplurality of the predetermined background object reference materialequivalent path length images from the overlap region in thedual-reference material equivalent path length images of the unknownobject to provide reference material equivalent path length imageshaving first and second reference material equivalent path lengthspassing through only the unknown object.

In another aspect, the background object is unknown and has a homogenouscomposition and thickness, the dual-energy attenuation imagesrepresenting the unknown object include pixels distributed in rows andcolumns and having dual-energy attenuation information, anddual-reference material equivalent path length images of the unknownobject include a background region with first and second referencematerial equivalent path lengths passing through only the backgroundobject and an overlap region with first and second reference materialequivalent path lengths passing through the unknown object overlappingwith the background object. The step of removing the reference materialequivalent path lengths representing the background object from thereference material equivalent path length images may further include thesteps of determining the background region and the overlap region byusing a segmentation algorithm to localize the background region,determining one of an average, a median and a mean of the first andsecond reference material equivalent path lengths passing through onlythe background object in each column, and, eliminating the one of theaverage, the median and the mean of the first and second referencematerial equivalent path lengths passing through only the backgroundobject from the first and second reference material equivalent pathlengths of each column of the overlap region to determine first andsecond reference material equivalent path lengths representing only theunknown object.

In another aspect, the background object is unknown and has a homogenouscomposition, the dual-energy attenuation images representing the unknownobject include pixels distributed in columns and rows and havingdual-energy attenuation information, and the dual-reference materialequivalent path length images of the unknown object include a backgroundregion with first and second reference material equivalent path lengthspassing through the background object and an overlap region with firstand second reference material equivalent path lengths passing throughthe unknown object overlapping with the background object. The step ofremoving the reference material equivalent path lengths representing thebackground object from the reference material equivalent path lengthimages further includes the steps of obtaining a three-dimensional modelof the background object according to the position and orientation ofthe background object as scanned in the x-ray scanning device,determining first and second reference material equivalent path lengthsthrough the background object in the three-dimensional model for eachpixel using a ray casting algorithm, determining the effective atomicnumber of each pixel in the dual-reference material path length imagesof the background object, determining the density of each pixel in thedual-reference material path length images of the background object,determining the mass thickness of the background object by multiplyingthe determined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject, localizing the background region and the overlap region in thedual-reference material path length images by using a segmentationalgorithm, eliminating the mass thickness of the background object fromthe mass thickness of the reference material path length images toobtain a mass thickness of the unknown object, and, determining thefirst and second reference material equivalent path lengths through theunknown object.

The step of determining the effective atomic number of the container mayfurther include the steps of identifying a pixel which has traversedonly a wall of the container, and, determining the effective atomicnumber associated with the attenuation information of the identifiedpixel as provided by the step of decomposing each of the dual-energyattenuation images into dual-reference material equivalent path lengthimages.

The step of determining container path lengths representing thecontainer may further include the steps of extending at least one of thefirst and second source-detector pair lines passing through the objectof interest from the inner contour of the container to the outer contourof the container using a ray casting algorithm, subtracting the extendedat least one of the first and second source-detector pair lines from thecorresponding at least one of the first and second source-detector pairlines to provide at least one of first and second source-detector pairline segments, and, determining a path length of the at least one offirst and second source-detector pair line segments.

In another aspect, the background object is a security screening tray,and after the step of interpolating the outer bound of the container todefine the outer contour of the container, the method further comprisesthe steps of, detecting the presence of an empty space within thecontainer, determining points of intersection representing a firstinterface between the object of interest and the empty space from pointsof intersection representing a second interface between the unknownobject and the container, reflecting the points representing the firstinterface and the points representing the container wall relative to anaxis that is parallel to a surface of the tray, eliminating points underthe axis, and, joining sections of the container contour usinginterpolation.

The method may further include the steps of evaluating a periodicity ofone of a container wall thickness and a radial size of the unknownobject, and, if the periodicity is regular, applying the periodicity tothe one of the container wall thickness and the radial size of theunknown object to determine the container wall thickness.

The step of determining the effective atomic number of the unknownobject may further include the steps of for path lengths on a supportingline passing through the unknown object and the background object,solving individually

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k)

for pairs of path lengths where o represents the object of interest, brepresents the background, ob represents the overlap region, pixels arerepresented by i, slices by j and views by k.

The step of determining the effective atomic number of the unknownobject may further include the steps of fitting linearly on thefollowing equations:

$\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{{\rho t}_{ob}\left( {i,j,k} \right)}{t_{b}}$$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}{{\rho t}_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}{{\rho t}_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$

wherein, the slope of the first equation is ρ_(o) and the slope of thesecond equation is g[Z_(o)]ρ_(o), and the intersection in the firstequation gives ρ_(b).

The step of determining the effective atomic number of the unknownobject may further include the steps of fitting on the followingbivariate linear functions:

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

with the regressors t_(o)(i,j,k) and t_(b)(i,j,k), and the predictorρt_(ob)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k),

-   -   and the predictor g[Z_(ob) (i,j,k)]ρt_(ob) (i,j,k)        wherein, for the first equation, the slope in direction x at y=0        is ρ_(b) and the slope in direction y at x=0 is ρ_(b), for the        second equation, the slope in direction x at y=0 is        g[Z_(o)]ρ_(o) and the slope in direction y at x=0 is        g[Z_(b)]ρ_(b), and, obtaining g[Z_(o)] can be by dividing        g[Z_(o)]ρ_(o) by the previously obtained ρ_(o), and Z_(o)        obtained with g⁻¹{g[Z_(o)]}.

In another aspect, there is provided a method for assigning attributesto an unknown object including the steps of scanning the unknown objectat least partially overlapping with a background object within an x-rayscanning device. The x-ray scanning device emits x-rays from at leasttwo sources which pass through the object of interest and the backgroundobject. The x-rays are detected by at least one array of detectors toprovide a plurality of dual-energy attenuation images each havingdual-energy attenuation information representing an overlap regionwherein the background object and the unknown object overlap. The methodfurther includes the steps of decomposing each of the dual-energyattenuation images into reference material equivalent path lengthimages, removing the reference material equivalent path lengthsrepresenting the background object from the reference materialequivalent path length images to provide reference material equivalentpath lengths representing the unknown object, converting the referencematerial equivalent path lengths representing the unknown object intounknown object path lengths multiplied by a predetermined scalingfactor, determining the mass thickness for each pixel representing theunknown object, the mass thickness being equivalent to the unknownobject path lengths multiplied by the scaling factor, identifying eachfirst source-detector pair line defined by a first x-ray extendingbetween a first one of the at least two sources and one detector of thearray of detectors in a first one of the plurality of dual-energyattenuation images on which lies one scaled unknown object path length,identifying each second source-detector pair line defined by a secondx-ray extending between a second one of the at least two sources and onedetector of the array of detectors in a second one of the plurality ofdual-energy attenuation images on which lies one other scaled unknownobject path length, the second one of the plurality of dual-energyattenuation images generated contemporaneously with the first one of theplurality of dual-energy attenuation images, joining the extremities ofeach of the scaled unknown object path lengths to provide a contour ofthe unknown object, iteratively matching the contour of the unknownobject of each of the first and the second one of the plurality ofdual-energy attenuation images to reduce the scaling factor of theunknown object path lengths and to provide unknown object path lengths,and, determining a density of the unknown object and an effective atomicnumber of the unknown object.

In one aspect, the step of decomposing the plurality of dual-energyattenuation images into reference material equivalent path length imagesfurther includes the steps of retrieving from lookup tables saveddual-reference material equivalent path lengths associated with thedual-energy x-ray attenuation information corresponding with thedual-energy attenuation images.

In another aspect, the step of decomposing the plurality of dual-energyattenuation images into reference material equivalent path length imagesmay further include the steps of scanning in the x-ray scanning device,first and second reference materials each having known atomiccomposition, known dimensions and known orientation in the x-rayscanning device. The x-ray scanning device emits x-rays which passthrough the first reference material with first reference material pathlengths and through the second reference material with second referencematerial path lengths to provide dual-energy x-ray attenuationinformation. The method further includes the steps of associating thedual-energy x-ray attenuation information for each pixel in thedual-energy attenuation images with each of the first reference materialpath lengths and the second reference material path lengths, expressingcollectively each of the first reference material equivalent pathlengths and the second reference material equivalent path lengths as afunction of the associated dual-energy x-ray attenuation information todefine dual-energy attenuation surfaces, and, imposing dual-energyattenuation information of the dual-energy images onto the dual-energyattenuation surfaces to determine corresponding first reference materialequivalent path lengths and second reference material equivalent pathlengths corresponding with the dual-energy attenuation information.

The dual-energy attenuation images may include low-energy attenuationimages and high-energy attenuation images, the dual-reference materialequivalent path length images may include first reference materialequivalent path length images and second reference material equivalentpath length images and the dual-energy x-ray attenuation information mayinclude high-energy x-ray attenuation information and low-energy x-rayattenuation information.

In one aspect, the expressing step further includes the step ofinverting numerically point-by-point the dual-energy attenuationsurfaces using an optimization algorithm to provide inverse dual-energyattenuation surfaces.

In another aspect, the expressing step further includes selecting amodel for expressing collectively each of the first reference materialequivalent path lengths and the second reference material equivalentpath lengths as a function of the associated dual-energy x-rayattenuation information to define dual-energy attenuation surfaces.

The step of selecting the model may further include the steps ofselecting a set of coefficients to be applied to the model for fittingthe dual-energy x-ray attenuation information with the model, and,fitting the dual-energy x-ray attenuation information with the model byoptimizing the coefficients.

The step of selecting the model may further include the steps ofselecting the set of fitting constraints to be applied to the model forselecting the coefficients, and, selecting the set of coefficients byapplying the set of fitting constraints to the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation, and the associating step may further include defining afirst space wherein the low-energy x-ray attenuation information of thefirst reference material and the second reference material defines afirst plane and first reference material equivalent path lengths andsecond reference material equivalent path lengths each define a firstheight over the first plane, defining a second space wherein thehigh-energy x-ray attenuation information of the first referencematerial and the second reference material defines a second plane andfirst reference material equivalent path lengths and second referencematerial equivalent path lengths each define a second height over secondthe plane, and, representing collectively the first reference materialequivalent path lengths and the second reference material equivalentpath lengths using the model to define the dual-energy attenuationsurfaces.

In another aspect, the model is a second model, the dual-energyattenuation surfaces are inverse attenuation surfaces, and prior to theassociating step, the method further includes the steps of associatingeach of the dual-energy x-ray attenuation information with correspondingones of each of the first reference material equivalent path lengths andthe second reference material equivalent path lengths, and, selecting afirst model for expressing collectively the dual-energy x-rayattenuation information as a function of the first reference materialequivalent path lengths and the second reference material equivalentpath lengths to define direct attenuation surfaces.

The step of selecting the first model may further include the steps ofselecting a first set of coefficients to be applied to the first modelfor fitting the dual-energy x-ray attenuation information with the firstmodel, and, fitting the dual-energy x-ray attenuation information withthe first model by optimizing the first coefficients. The step ofselecting the second model may further include the steps of selecting asecond set of coefficients to be applied to the second model for fittingthe dual-energy x-ray attenuation information with the second model,and, fitting the dual-energy x-ray attenuation information with thesecond model optimizing the second set of coefficients.

The of selecting the first model may further include the steps ofselecting a first set of fitting constraints to be applied to the firstmodel for selecting the first set of coefficients, and, selecting theset of first coefficients by applying the first set of fittingconstraints to the first model. The step of selecting second the modelfurther includes the steps of selecting a second set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients, and, selecting the second set of coefficients byapplying the second set of fitting constraints to the second model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the associating may further include the steps ofdefining a space wherein the first reference material equivalent pathlengths and the second reference material equivalent path lengths definea first plane and the high-energy x-ray attenuation information and thelow-energy x-ray attenuation information each define a respective firstand second height over the first plane and represent collectively thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information using the first model to define the directattenuation surfaces, and, defining an inverse space wherein thelow-energy x-ray attenuation information and the high-energy x-rayattenuation information define a second plane and first referencematerial equivalent path lengths and second reference materialequivalent path lengths each define a respective third and fourth heightover the second plane and representing collectively the first referencematerial equivalent path lengths and the second reference materialequivalent path lengths using the second model to define the inverseattenuation surfaces.

The method may further include the steps of determining the mass densityof each of the first and second reference materials, determining aproduct of the first reference material equivalent path lengths and themass density of the first reference material to provide a firstreference material mass thickness, determining a product of the secondreference material equivalent path lengths and the mass density of thesecond reference material to provide a second reference material massthickness, and, determining a total reference material mass thickness bysumming the first reference material mass thickness and the secondreference material mass thickness.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation, and the step of decomposing may further include the stepsof, for each of the first and second reference materials, determining anenergy-dependent attenuation cross section based on each of thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information, defining a Z_(eff)-dependent cross-sectionwherein a Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation, evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections,re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror, and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to each of the first andsecond reference materials.

The step of determining the energy-dependent attenuation cross sectionbased on each of the low-energy x-ray attenuation information and thehigh-energy x-ray attenuation information may further include the stepof, for each of the first and second reference materials, determining atleast one of an average, a median and a mean of energy-dependentattenuation cross-sections per mol of electron of each element in thereference material, weighted by the total number of electrons of eachelement in the reference material.

The step of determining the one of the average, the median and the meanenergy-dependent attenuation cross-section per mol of electron of eachelement in the reference material may further include the steps of, foreach of the first and second reference material, determining the productof a known mass attenuation coefficient of the reference material and amolar mass over the number of electrons per unionized atom of eachelement in the reference material.

The step of defining Z_(eff)-dependent cross-section may further includethe step of, for each of the first and second reference materials,determining a linear combination of energy-dependent attenuationcross-sections of each of the two elements having atomic numbersimmediately adjacent to the effective atomic number value on which theZ_(eff)-dependent cross-section is based.

The step of evaluating an energy-dependent material transmittancefunction may further include, for each of the first and second referencematerials, evaluating an inverse exponential function of an electrondensity of the reference material and the energy-dependent attenuationcross-section of the reference material.

The step of minimizing the low-energy level domain weighted squaredtransmission error may further include the step of, for each of thefirst and second reference materials, integrating a weighted differencebetween the energy-dependent material transmittance function and thecorresponding Z_(eff)-dependent material transmittance function.

The step of converting the reference material equivalent path lengthsrepresenting the unknown object into unknown object path lengthsmultiplied by a predetermined scaling factor may further include thestep of applying the following function for each of the first and secondreference material equivalent path lengths representing the unknownobject:

${t_{o}\left( {i,j} \right)} = {\frac{{\rho t}_{ob}\left( {i,j} \right)}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}$$\begin{matrix}{{t_{o}^{*}\left( {i,j} \right)} = {{{\rho t}_{ob}\left( {i,j} \right)}\left( {{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right) \times {scaling}\mspace{14mu} {factor}}} \\{= {{{t_{o}\left( {i,j} \right)} \times {scaling}\mspace{14mu} {factor}} = {{t_{o}\left( {i,j} \right)} \times {SF}}}}\end{matrix}$${{With}\mspace{14mu} {SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}{when}\mspace{20mu} {t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}$

wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants.

The dual-energy attenuation information may include high-energyattenuation information and low-energy attenuation information and thestep of determining the effective atomic number of the unknown objectmay further include the steps of determining a first weight fraction ofeach of the first and second reference materials in the unknown object,determining a second weight fraction of each element of each of thefirst and second reference materials in the unknown object, determininga mass attenuation coefficient of the unknown object, determining anenergy-dependent attenuation cross section of the unknown object,defining a Z_(eff)-dependent cross-section of the unknown object whereina Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation, evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections,re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror, and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to the unknown object.

The step of determining the mass attenuation coefficient for the unknownobject may further include the steps of determining an effective weightfraction of each element of each reference material in the unknownmaterial, determining a mass attenuation coefficient of each element ofeach reference material in the unknown material, and, determining aproduct of the effective weight fraction and mass attenuationcoefficient of each element of each reference material in the unknownmaterial.

In one aspect, the background object is a predetermined backgroundobject, and the step of removing the reference material equivalent pathlengths representing the background object from the reference materialequivalent path length images may further include the steps of scanningthe predetermined background object in a plurality of positions andorientations within an x-ray scanning device to obtain a plurality ofpredetermined background object dual-energy attenuation images eachhaving predetermined background object dual-energy attenuationinformation representing the predetermined background object,decomposing the predetermined background object dual-energy attenuationimages into predetermined background object dual-reference materialequivalent path length images having predetermined background objectreference material equivalent path lengths passing through thepredetermined background object, determining the position andorientation of the background object in one of the dual-energyattenuation images and the dual-reference material equivalent pathlength images of the unknown object by using a segmentation algorithm tolocalize the background object, determining, by comparison,corresponding ones of the plurality of predetermined background objectreference material equivalent path length images which most closelycorresponds with the position and orientation of the background objectin the dual-reference material equivalent path length images, and,eliminating the predetermined background object reference materialequivalent path lengths of the corresponding ones of the plurality ofthe predetermined background object reference material equivalent pathlength images from the overlap region in the dual-reference materialequivalent path length images of the unknown object to provide referencematerial equivalent path length images having first and second referencematerial equivalent path lengths passing through only the unknownobject.

In another aspect, the background object is unknown and has a homogenouscomposition and thickness, and the dual-energy attenuation imagesrepresenting the unknown object include pixels distributed in rows andcolumns and have dual-energy attenuation information, and dual-referencematerial equivalent path length images of the unknown object include abackground region with first and second reference material equivalentpath lengths passing through only the background object and an overlapregion with first and second reference material equivalent path lengthspassing through the unknown object overlapping with the backgroundobject. The step of removing the reference material equivalent pathlengths representing the background object from the reference materialequivalent path length images further includes the steps of determiningthe background region and the overlap region by using a segmentationalgorithm to localize the background region, determining a mean of thefirst and second reference material equivalent path lengths passingthrough only the background object in each column, and, eliminating themean of the first and second reference material equivalent path lengthspassing through only the background object from the first and secondreference material equivalent path lengths of each column of the overlapregion to determine first and second reference material equivalent pathlengths representing only the unknown object.

In another aspect, the background object is unknown and has a homogenouscomposition, the dual-energy attenuation images representing the unknownobject include pixels distributed in columns and rows and havingdual-energy attenuation information, and the dual-reference materialequivalent path length images of the unknown object include a backgroundregion with first and second reference material equivalent path lengthspassing through the background object and an overlap region with firstand second reference material equivalent path lengths passing throughthe unknown object overlapping with the background object. The step ofremoving the reference material equivalent path lengths representing thebackground object from the reference material equivalent path lengthimages may further include the steps of obtaining a three-dimensionalmodel of the background object according to the position and orientationof the background object as scanned in the x-ray scanning device,determining first and second reference material equivalent path lengthsthrough the background object in the three-dimensional model for eachpixel using a ray casting algorithm, determining the effective atomicnumber of each pixel of the dual-reference material path length imagesof the background object, determining the mass density of each pixel ofthe dual-reference material path length images of the background object,determining the mass thickness of the background object by multiplyingthe determined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject, localizing the background region and the overlap region in thedual-reference material path length images by using a segmentationalgorithm, eliminating the mass thickness of the background object fromthe mass thickness of the reference material path length images toobtain a mass thickness of the unknown object, and, determining thefirst and second reference material equivalent path lengths through theunknown object.

The step of determining the effective atomic number of the unknownobject may further include the steps of, for path lengths on asupporting line passing through the unknown object and the backgroundobject, solving individually:

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k)

for pairs of path lengths where o represents the object of interest, brepresents the background, ob represents the overlap region, pixels arerepresented by i, slices by j and views by k.

The step of determining the effective atomic number of the unknownobject may further include the step of, fitting linearly on thefollowing equations:

$\frac{{\rho t}_{ob}\left( {i,j,k} \right)}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{{\rho t}_{ob}\left( {i,j,k} \right)}{t_{b}}$$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}{{\rho t}_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}{{\rho t}_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$

wherein, the slope of the first equation is ρ_(o) and the slope of thesecond equation is g[Z_(o)]ρ_(o), and the intersection in the firstequation gives ρ_(b).

The step of determining the effective atomic number of the unknownobject may further include the steps of fitting on the followingbivariate linear functions:

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k), and the predictorρt_(ob)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k),

-   -   and the predictor g[Z_(ob)(i,j,k)]ρt_(ob)(i,j,k)        wherein, for the first equation, the slope in direction x at y=0        is ρ_(o) and the slope in direction y at x=0 is ρ_(b), for the        second equation, the slope in direction x at y=0 is        g[Z_(o)]ρ_(o) and the slope in direction y at x=0 is        g[Z_(b)]ρ_(b), and, obtaining g[Z_(o)] can be by dividing        g[Z_(o)]ρ_(o) by the previously obtained ρ_(o), and Z_(o)        obtained with g⁻¹{g[Z_(o)]}.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of an exemplary x-ray scanning device whichmay be used in association with the present invention;

FIG. 2 is an illustration of a system which may be used in associationwith the present invention;

FIG. 3 is a flow chart representing the calibration method of thepresent invention;

FIG. 4 is a flow chart representing the method for modeling ofdual-material equivalent path lengths as a function of the dual-energysignal as shown in FIG. 3;

FIG. 5 is an example plane wherein the dual-energy x-ray attenuationsmeasured by a detector are represented on the z axis, the first materialpath length values t₁ are represented on the x axis and the secondmaterial path length values t₂ are represented on the y axis;

FIG. 6 is an example three-dimensional space wherein the referencematerial path length values for each pixel representing the referencematerials define a plane and wherein a z-axis also represents thecorresponding measured HE and LE x-ray attenuation as a height off ofthe plane;

FIG. 7 shows an example step wedge as may be used in association withthe present invention;

FIG. 8 shows a fitted direct attenuation surface with data points usedfor the fitting for the low-energy domain;

FIG. 9 shows a fitted direct attenuation surface with data points usedfor the fitting for the high-energy domain;

FIG. 10A shows an inverted attenuation surface for the first referencematerial path lengths t₁;

FIG. 10B shows an inverted attenuation surface for the second referencematerial path lengths t₂;

FIG. 11 is a flow chart representing the method for assigning effectiveatomic number values to the first and second reference materialattenuation as shown in FIG. 3;

FIG. 12 is a flow chart representing the method for assigning massthickness to the first and second reference material attenuation asshown in FIG. 3;

FIG. 13 is a flow chart representing the method for assigning aneffective atomic number value to an unknown object;

FIG. 14 is a flow chart representing one aspect of a method for removinga predetermined background object from an image;

FIG. 15 is an example representation of the object and background pathlengths showing an overlap region;

FIG. 16 is a flow chart representing another aspect of method forremoving a background object from an image;

FIGS. 17A & B are a flow chart representing another aspect of method forremoving a background object from an image;

FIG. 18 is a flow chart representing one aspect of a method forextending a range of calibration information;

FIG. 19 is a representation of the method shown in FIG. 18;

FIG. 20 is another aspect of the method for extending a range ofcalibration information;

FIG. 21 is another aspect of the method for extending a range ofcalibration information;

FIG. 22 is a representation of the method shown in FIG. 21;

FIGS. 23A & B are a flow chart representing one aspect of a method forreconstructing an unknown object contained within a container;

FIG. 24 is a flow chart representing one aspect of a method for removinga background object as part of the method for reconstructing an unknownobject;

FIG. 25 is a flow chart representing another aspect of a method forremoving a background object as part of the method for reconstructing anunknown object;

FIG. 26 is a flow chart representing one aspect of a method forreconstructing an unknown object; and,

FIG. 27 is a flow chart representing one aspect of a method fordetermining a safe of threat condition for an unknown object.

DESCRIPTION

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

The present invention provides methods and apparatuses which aresuitable for detection of potentially harmful objects scanned in anx-ray scanning device which provides for automatic and real time or nearreal time analysis of the information provided.

According to the aspect shown in FIG. 1, there is provided an x-rayscanning device 100. The x-ray scanning device 100 includes a housing102 having openings 104 at either end thereof. The openings 104 provideaccess to a scanning chamber 106 passing through the housing 102. Thesystem 100 may further include a displacement assembly 108, such as aconveyor, which extends through the scanning chamber 106 and which maybe used to displace at least one object of interest to be scanned usingthe x-ray scanning device 100.

The term “object” as used herein refers to any object of interest, knownor unknown, for scanning purposes and is not necessarily limited to aspecific shape, size, composition or configuration. The object ofinterest may be a singular object composed of one or more materials,such as for example, a liquid material contained within a container, ormay include a plurality of objects targeted for scanning, such as forexample, the contents of a bag of luggage.

The x-ray scanning device 100 further includes a source assembly 110.The source assembly 110 includes a source (not shown) for emittingelectromagnetic radiation such as x-rays, a source assembly housing 112at least partially enclosing the source, a pedestal 114 to which thesource assembly housing 112 is mounted and a collimator 116 mounted tothe source assembly housing 112 for directing x-rays emitted from thesource. Collimator 116 may be of any suitable shape but is preferably afan-shaped collimator for directing the x-rays in a fan-shaped beam.Moreover, the pedestal 114 is not required and may not necessarily bepresent in some x-ray scanning devices suitable for the purposes of thepresent invention.

The x-ray scanning device 100 may further include a group of detectorsincluding at least one detector card 120 and preferably a plurality ofdetector cards 120 each mounted to the bracket 122. It should beunderstood to a person skilled in the art that the detector may be in aform other than a detector card that would be suitable for the purposesof the present invention. In one aspect, the bracket is an L-shapedbracket which is positioned outside the scanning chamber 106 such thatthe plurality of detector cards 120 mounted thereto extend into thescanning chamber 106. In some aspects, the bracket 122 may be locatedwithin the scanning chamber. In the aspect shown in FIG. 1 there isshown mounted within the scanning chamber a single bracket 122. Itshould be understood that in other aspects, the scanning chamber mayinclude more than one bracket positioned within the scanning chamber andthat the brackets do not have to have the same orientation or angularposition. It should be further understood that the bracket 122 does nothave to be L-shaped. Rather, the bracket 122 may be linear or arc shapedor any other suitable shape.

In some embodiments, each detector card 120 includes at least oneindividual detector. As shown in FIG. 2, detector cards 120 and thex-ray scanning device 100 may be linked to a central processing unit(CPU) 200 or other processing device so that x-ray signals detected bythe detector cards 120 may be analyzed, processed, and used to outputinformation, is further disclosed herein. The processor 200 and itsassociated architecture may be used to implement any of the processes ormethods described herein as well as one or more of their associatedsteps either automatically or in real-time or both.

According to the aspect shown in FIG. 2, each detector card 120 maycomprise a first scintillator material 202, a filter 204 and a secondscintillator material 206. All of these may be sandwiched together orotherwise suitably arranged as shown in FIG. 2. In a scanning operation,broad x-ray spectral intensity is emitted by the source and is directedby the collimator 116 toward the plurality of detector cards 120 withinthe scanning chamber 106. In the case of each detector card 120, aplurality of the emitted x-rays encounter the first scintillatormaterial 202 which may be configured to detect preferentially the lowerportion of the emitted x-ray spectral intensity. The spectral intensityof x-rays may then be stopped by the filter 204 and remaining x-rays'spectral intensity reach the second scintillator material 206. Due tothe transmission through the first scintillator material 202 and thefilter 204, the x-rays spectral intensity reaching the secondscintillator material 206 contains a higher portion of high-energyx-rays than the x-rays spectral intensity reaching the firstscintillator material 202.

In the context of the present description, the term “processor” refersto at least one computerized component for executing computer-executableinstructions. This may include, for example, a central processing unit(CPU), a microprocessor, a controller, and/or the like. A plurality ofsuch processors may be provided, according to different aspects of thepresent invention, as can be understood by a person skilled in the art.The processor may be provided within one or more general-purposecomputers, for/or any other suitable computing device.

The term “storage” may refer to any computer data storage device orassembly of such devices including, for example, a temporary storageunit such as random-access memory (RAM) or dynamic RAM, permanentstorage medium such as a hard disk, and optical storage device, such asa CD or DVD (rewritable or write once/read only), a flash memory, adatabase, and/or the like. A plurality of such storage devices may beprovided, as can be understood by a person skilled in the art.

With further reference to FIG. 2, in one aspect, each of thesescintillator materials 202, 206 converts the absorbed x-ray energy toinfrared, visible and ultraviolet light. Each of these scintillatormaterials 202, 206 is coupled with a photodiode 208 which captures thelight from the respective scintillator 202, 206 and generates acorresponding analog electric signal. The analog electric signal isfurther digitized by a converter 210. The digitized signal value isassociated with a pixel of an image for providing a visualrepresentation of an object being scanned.

In the conversion of the infrared, visible and ultraviolet light into ananalog electric signal by the photodiodes 208, some uncertainties may beintroduced, in that a given x-ray spectral intensity may result in adifferent infrared, visible and ultraviolet light source which may alsoresult in different analog electric signals due to the fact that everydetector in every detector card may react slightly differently to thepresence of electromagnetic radiation. Slight variations in the x-rayand/or light sources may be taken into account in all methods describedherein. In order to correct these variations and for the final image toappear more homogeneously, each pixel of the image may be normalized bycorrecting an offset and gain in the light conversion. The normalizationprocedure may be executed for example using a normalization module 212as shown in FIG. 2 in order to compensate for slight variations inoffset and gain for each detector, as well as for estimating theexpected uncertainties in low-energy and high-energy signals and/orattenuations for each detector.

The apparatus may further include a dual-material decomposition module214 for decomposing low-energy and high-energy signals and/orattenuations of known or unknown scanned materials into correspondingreference material attribute information, a mass thickness determinationmodule 216 for determining the mass thickness of one or more objects ofinterest, an effective atomic number module 218 for determining theeffective atomic number of one or more objects or materials of interest,a background removal module 220 for distinguishing one object ormaterial from another in a dual-energy image and removing high andlow-energy x-ray signal information associated with specific objectswhich may not necessarily be of interest, a reconstruction module 222for reconstructing an object of interest once high and low-energy x-raysignal information associated with the specific not-of-interest objectshave been removed and a threat determination module 224 for determiningwhether one or more objects or materials of interest pose a threat andcorrespondingly raising an alarm condition based on the determination.Information acquired by any of the aforementioned modules may be savedto a suitable storage medium such as a database 226. Moreover, imagesmay be output to a display 228.

Calibration Method

This calibration method described herein is directed to acquiringreference data and deriving values representative of the real-world usedfor the purpose of computing images representing physical properties ofscanned objects from dual-energy transmission images.

In one aspect, the source emits x-rays across an energy spectrum, from 0keV to the energy corresponding to the peak voltage of the source. Thepeak voltage may be, for example, 160 kVp. The spectrum S(E) is afunction taking, in general, non-zero positive values all over theenergy range 0 keV to 160 keV. This spectrum will be detected by twoarrays of detectors stacked on top of each other. The array closest tothe source is the low-energy (LE) detector and preferentially absorbsx-rays with low-energies among all the energies available in thespectrum. The x-rays that are not absorbed by the LE detectors, passthrough the LE detectors and those which are not filtered out by thefilters reach the high-energy (HE) detectors, which absorbs x-rays withhigher energies due the hardening of the spectral intensity of thex-rays. The materials composing the detectors may also induce adifference in the energies they absorb. The low-energy x-ray signals andthe high-energy x-ray signals may be collectively referred to as“dual-energy signals”. Likewise, properties of or derived independentlyfrom both high-energy x-ray signals and low-energy x-ray signals, suchas attenuation or images, for example, may likewise be referred to as“dual-energy”. Moreover, since a detector includes both high-energy andlow-energy detectors, the detectors themselves may sometimes be referredto as “dual-energy detectors”. A person skilled in the art willappreciate that dual-energy signals can also be generated by othermeans, such as switching the peak voltage of the source or by using twosources, but different fixed peak voltages. In these embodiments, onlyone scintillator material for each of the detector arrays associatedwith each of the source would be required to acquire the dual-energysignals.

The method described herein includes decomposing dual-energy x-rayattenuation images into reference material path length images.Preferably, two reference materials are used to provide the basis forthe reference material path length images. Accordingly, the set ofimages provided by the two reference materials may be collectivelyreferred to as the “dual-material” or the “reference material” pathlength images. The reference material path length images allow thefurther computation of both the mass thickness and effective atomicnumber of an object of interest. The mass density of the object ofinterest may then be deduced from the mass thickness and the pathlengths of the object of interest. The dual-material path lengthdecomposition approach includes the acquisition of reference data fromreference objects, such as step wedges, composed of two differentmaterials scanned in several different configurations and orientationswithin the scanning device, as is discussed in further detailhereinafter. FIG. 7 shows an example step wedge composed of 2 plates ofABS stacked on top of 8 plates of Aluminum. The materials composing thestep wedges may include any homogeneous material such as, for example,plexiglass, aluminum and/or steel. The step wedge materials arepreferably in the form of plates which may have different lengths andthicknesses but each plate is preferably of uniform thickness. Anexample step wedge may include 10 steps built by stacking plates made oftwo basis materials on top of each other or otherwise suitably arranged.The steps in the step wedge may be varied in their composition bychanging the stacking order of the plates of material and the number ofplates of each basis material used in the assembly. For the purposes ofproviding a basis for decomposition of x-ray attenuation images intoreference material path length images, the dual-material step wedges areof known configuration and thickness and are composed of known materialshaving known atomic composition and mass density. The thickness of eachstep in the step wedge may be measured directly on the step wedge usinga measurement tool such as a caliper. Also known are the relativepositions of the detectors with respect to their associated source. Thisinformation is available from the mechanical design of the x-ray scanneror may be determined by other suitable means.

Assignment of Path Lengths to Reference Materials

In a first aspect as shown in FIG. 3, there is provided a method 300 forassigning an attribute, such as reference material path lengths, tox-ray attenuation information. In a first step 302, dual-referencematerials are scanned, such as a dual-material step wedge havingcomposed of first and second reference materials, preferably in morethan one orientation, such as flat on the conveyor belt or on one of itssides and in more than one position within the x-ray scanner such thatall active detectors detect the profile of the step wedge in at leastone position. Thereby, there is provided dual-material calibration dataas in step 304. During each scan of the dual-material step wedge, x-rayspass through the dual-material step wedge to be detected by detectors.The detected x-rays produce dual-energy x-ray signals, which may includelow-energy x-ray signals and high-energy x-ray signals. These signalsmay be used to generate a high-energy (HE) domain image and a low-energy(LE) domain image. Together, the high-energy domain image and thelow-energy domain image may be referred to as a “dual-energy image” or a“set of dual-energy images”. Each of the high-energy domain image andthe low-energy domain image is composed of a plurality of pixelsdistributed in columns and rows. Each high-energy domain image andlow-energy domain image of the scanned dual-material step wedges may besaved in a suitable storage medium such as an information database.

In each LE domain image and/or HE domain image, there will be determineda region-of-interest (ROI). The ROI represents the pixels of the LE orHE domain image representing the scanned step wedge The ROI may excludeamong other things the transitions between the steps of the step wedgeand other parts of the step wedge used to ensure its mechanicalintegrity such as, for example, bolts, nuts and sustaining rack. In viewof this, it should be understood that the entire image or parts of itmay be considered as a whole in order to determine information morecomplex than that provided by a single pixel.

A path length is the length of the path of an x-ray directed from thesource focal point passing through the material to a given detector.Since the thickness of each material of the dual-material step wedge isknown, the orientation of the dual-material step wedge within the x-rayscanner is known and the position of the source and all active detectorsis known, the path length of the x-rays through material may becalculated for all active detectors. In one aspect, these calculatedvalues may further be placed in a database for storing step wedgematerial path length values for later retrieval.

The reference material path lengths are mathematical variables derivedfrom the low-energy x-ray attenuation and high-energy x-ray attenuationwhich corresponds with the path length of the x-rays through acorresponding location in the reference material. The reference materialpath lengths through a scanned material may be represented usingnotation t_(m), m=1,2. For scanned reference materials, the first andsecond reference material path lengths are measured and take specificknown values denoted as {circumflex over (t)}_(m), m=1,2. Therefore, thefirst reference material path length t₁ may take corresponding measuredfirst reference material path length values {circumflex over (t)}₁. Thesecond reference material path length t₂ may take corresponding measuredsecond reference material path length value {circumflex over (t)}₂.Further use of the expressions “first material path lengths” and “secondmaterial path lengths” may refer to either the mathematical variablest_(m), m=1,2 derived from the low-energy x-ray attenuation andhigh-energy x-ray attenuation or the corresponding known (measured)values {circumflex over (t)}_(m), m=1,2, as a person skilled in the artwould recognize.

The dual reference material path length values t₁ and t₂ may then beassociated or modeled in step 306 as a function of the measured high andlow-energy x-ray attenuation values. In general, the high and low-energyattenuation A associated with the high and low-energy normalized signalI is given by

$A = {- {\ln \left( \frac{I}{R} \right)}}$

where R is an arbitrary strictly positive constant called thenormalization range and is equal to the normalized signal when no objectis scanned. In view of this, it should be understood to a person skilledin the art that the low-energy or high-energy signal I and low-energy orhigh-energy attenuation A may be used interchangeably by a personskilled in the art, and may be used interchangeably herein, withoutdeparting from the scope of the invention.

Once the dual reference material path length values are modeled as afunction of the dual-energy signal, as in step 306, the values may besaved in corresponding lookup tables for more efficient determination ofthe equivalent path lengths of the first reference material associatedwith a particular x-ray attenuation as in step 308 and for the pathlengths of the second reference material as in step 310. It should beunderstood that “equivalent’ does not necessarily mean perfect physicalor geometric equivalence. The term “equivalent” as used herein may referto close approximation or modeling of the actual physical characteristicof a physical material or object, such as, for example, x-ray pathlengths, effective atomic number and mass thickness. As with any modeledphysical characteristic, there may be a slight difference between themeasured physical characteristic and the modeled physicalcharacteristic. The method may then proceed to step 312 wherein the pathlength information may be used as a basis for assigning mass thicknessvalues to the dual-energy x-ray attenuation for each of the referencematerials. Such mass thickness values may likewise be saved in massthickness lookup tables as in step 314 for more efficient determinationof the mass thickness values associated with dual-energy x-rayattenuation associated with each of the first and second referencematerials. Step 312 is discussed in further detail hereinafter. Once thefirst and second reference material path lengths are associated withspecific x-ray energy attenuation information provided by scanning thefirst and second reference materials, the first and second referencematerial path lengths may be used to subsequently determine anappropriate effective atomic number, or Z_(eff), to be assigned to thecorresponding x-ray attenuation information as in step 316. This step isdiscussed in further detail hereinafter. Moreover, it should beunderstood that this step 316 may be performed in advance of, inconjunction with or independently of step 312. The associated effectiveatomic number values may be saved in lookup tables for more efficientreference in future operations as shown in step 318.

The step 306 for modeling of the dual-material equivalent path lengthsas a function of the dual-energy attenuation signal is further definewith reference to FIG. 4 wherein a three-dimensional space may then bedefined for each of the measured high and low-energy x-ray signalswherein material path length values t₁ through the first material andmaterial path length values t₂ through the second material define points(t₁, t₂) forming a plane and each of the corresponding measured high andlow-energy x-ray attenuations each define a height over the plane. Thereis thereby provided a first three-dimensional space for high-energyx-ray attenuation and second three-dimensional space low-energy x-rayattenuation. An example plane is shown in FIG. 5 wherein the high-energyand low-energy x-ray attenuations measured by a detector are representedon the z-axis, the path length values t₁ through the first material arerepresented on the x-axis and the path length values t₂ through thesecond material are represented on the y-axis. An examplethree-dimensional space is shown in FIG. 6 wherein the referencematerial path length values for each pixel representing the referencematerials define a plane as in FIG. 5, but wherein a z-axis alsorepresents the corresponding measured HE and LE x-ray attenuation forthat detector as a height off of the plane.

At step 320, a first mathematical model is selected which is a functionto collectively represent the measured high-energy x-ray attenuations ofat least one of the detectors and collectively represent the low-energyx-ray attenuations of the at least one of the detectors in terms of thematerial path length values t_(m) for each of the basis materials m=1,2.A suitable mathematical model can be selected to represent bothhigh-energy x-ray attenuations and low-energy x-ray attenuations, theonly difference being the value of the coefficients that best fithigh-energy x-ray attenuations and low-energy x-ray attenuations. Aninitial set of coefficients including at least one coefficient may thenbe selected for initializing the model for fitting the low-energy x-rayattenuations and the high-energy x-ray attenuations with the model. Thesets of coefficients may be identified using vector notation {rightarrow over (c)}^(E) where E=LE, HE represents the energy level of themeasured low and high-energy x-ray signals. The initial set ofcoefficients includes at least one coefficient which could potentiallybe applied to the model depending on the conditions of the scanningoperation.

A mathematical model such as, for example, a Pade's approximant would besuitable.

A set of fitting constraints may also be applied to the mathematicalmodel for selecting the coefficients reflecting the actual physicalbehavior of the direct attenuation surfaces. These constraints force allthe fitting coefficients to respect certain mathematical expressionsrepresenting real-world physics in order to assure that the inverseattenuation surfaces could be obtained and will be physicallymeaningful.

The data set representing the high and low-energy x-ray attenuationsÂ^(E)(t₁, t₂) may be fitted with the model A^(E)(t₁, t₂; {right arrowover (c)}^(E)) using an optimization algorithm as in step 322 and thefitting constraints to define the direct attenuation surfaces withintheir respective three-dimensional space as shown in steps 326 and 328,respectively. Fitted direct attenuation surfaces 800, 900 with datapoints used for the fitting for the LE and HE domains are shown,respectively, in FIGS. 8 and 9. The optimization algorithm determinesthe coefficients which provide the strongest correlation between themodel and the collective measured high and low-energy x-ray attenuationsiteratively starting with the selected initial set of coefficients. Thismay involve changes to the coefficients as the optimization algorithm isapplied until an optimum is reached and/or the coefficients stopschanging significantly. Such a determination of the coefficients may bemade on the basis of, for example, a least-squares analysis or any othersuitable method. Such a determination of the coefficients may also takeadvantage of known measurement uncertainties in dual-energy attenuationsand/or dual-material path length to weight the fitting points in asuitable way. In other words, the coefficients applied to the model arethose which provide the closest representation of all of the measuredhigh and low-energy x-ray attenuations collectively by the model in therespective three-dimensional space. The direct attenuation surface istherefore the representation or expression of the collective measuredhigh and low-energy x-ray attenuations provided by the model for therespective energy domain image. Such a representation may, for example,be a high-energy and a low-energy three-dimensional surface 600 relatedclosely to the measured high and low-energy x-ray attenuations as shownin FIG. 6.

The coefficients optimized for the model may be saved in a database asshown in step 324 to be used in further operations. This provides anadvantage whereby the potentially computationally intensive step ofdetermining the coefficients can be avoided.

An inverted three-dimensional space may then be defined for path lengthsof the first and the second material wherein the measured high andlow-energy x-ray attenuations define a second plane and the associatedpath lengths for the x-rays passing through the respective material eachdefine a height off of the second plane. At step 330, a second model isselected which is a function to collectively represent the firstreference material path lengths and second reference material pathlengths as a function of the associated low-energy x-ray attenuationsand high-energy x-ray attenuations to each define an invertedattenuation surface as shown in steps 332 and 334. Inverted attenuationsurfaces 1000, 1100 for each of t₁ and t₂ are shown, respectively, inFIGS. 10 and 11. As with the first mathematical model, a second set ofcoefficients including at least one second coefficient may be applied tothe second model for fitting the low-energy x-ray attenuations andhigh-energy x-ray attenuations with the second model. A second set offitting constraints including at least one second fitting constraint mayalso be applied to the second model for selecting the secondcoefficients. Once again, an optimization algorithm may be used, asshown in step 336, to determine the “best fit” second set ofcoefficients for fitting the low-energy x-ray attenuations andhigh-energy x-ray attenuations with the second model. From the invertedattenuation surfaces, the path lengths through each of the two referencematerials may be determined when an imposed low-energy x-ray attenuationvalue and high-energy x-ray attenuation value is imposed to the inverseattenuation surface. First and second reference material path lengthvalues associated with high and low-energy x-ray attenuation values maybe saved in lookup tables as shown in steps 308 and 310, respectively,for later reference, although the steps 308 and 310 are not necessarilyrequired for the purposes of the method described herein. The method mayalso totally avoid the use of the second model and determine numericallypointwise inverted surfaces using an optimization algorithm invertingthe attenuation surfaces, as shown in FIGS. 10 and 11. Alternatively, asecond model may be selected for expressing the pointwise invertedsurfaces as a function low-energy x-ray attenuation and the high-energyx-ray attenuation to define inverted attenuation surfaces.

It is preferable to first fit the first model with the firstcoefficients to define the direct attenuation surfaces and then providethe respective inverse attenuation surfaces within the invertedthree-dimensional space using the second mathematical model as describedabove since this is the more numerically accurate and physicallyinterpretable method of determining the “best fit” coefficients.However, it should be understood that in a second aspect, once themeasured low-energy and high-energy x-ray attenuations are associatedwith each of the first material path lengths and second material pathlengths as in the aforementioned method, the method may then proceeddirectly to the step of selecting the second model to collectivelyrepresent all of the first and second material path lengths asrespective heights off of the second plane to define the inverseattenuation surface. The second coefficients and the second set offitting constraints may be used with an optimization algorithm todetermine the coefficients directly for the inverted attenuationsurfaces without having to first define the direct attenuation surfaces.

There is thereby provided an association between the high-energy andlow-energy x-ray attenuation values provided by scanning first andsecond reference materials and corresponding first and second referencematerial path lengths. Using the aforementioned method, the materialpath lengths through each of the first and second reference materialsmay be determined when at least one low-energy and high-energy x-rayattenuation value is imposed to the inverted attenuation surface. Anypair of high-energy and low-energy x-ray attenuation values imposed onthe inverted attenuation surface corresponds to a single path lengthvalue through each of the first material and the second material. Thepath length information provided by the inverted attenuation surface maybe saved in an information database such as in a dual-material pathlength look-up table for use in future operations relating tocalibration or other operations whereby it would be useful to determinethe path length of basis materials directly from measured x-rayattenuation values in the high and/or low-energy image domains.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Z_(eff) to Reference Material Attenuation Information

The step 316 of effective atomic number lookup table generation isdiscussed in further detail with reference to FIG. 11. Once the firstand second reference material equivalent path lengths are associatedwith specific x-ray energy attenuation information provided by scanningthe reference materials, as in step 306, reference material equivalentpath lengths may be used to subsequently determine an appropriateeffective atomic number, or Z_(eff), to be assigned to the correspondingx-ray attenuation information.

If the contribution of scattered X-rays to the raw signals reaching adual-energy detector after having passed through a certain length of anhomogeneous material M (also called a path length) are neglected, and ifit is assumed that the density and atomic composition are constantthroughout the material, the dual-energy signal, preferably a normalizeddual-energy signal, may be evaluated by integrating a weightedtransmittance function of the material over the incident X-ray energy:

I _(M) ^(E)(t _(M))=R∫ ₀ ^(∞) W ^(E)(E′)T _(M)(ρ_(M) ,t _(M) ,E′)dE′

I_(M) ^(E) represents the X-ray signal intensity, R is a normalizationconstant, W^(E) is a weighting function, T_(M) us the transmittancefunction of the material M, E′ is the X-ray energy, t_(M) is the pathlength trough the material and ρ_(M) is the material mass density.

The weighting function used is energy dependent, and will therefore varydepending on the X-ray source and detectors used:

${W^{E}\left( E^{\prime} \right)} = \frac{E^{\prime}{D^{E}\left( E^{\prime} \right)}{S\left( E^{\prime} \right)}}{\int_{0}^{\infty}{E^{\prime}{D^{E}\left( E^{\prime} \right)}{S\left( E^{\prime} \right)}{dE}^{\prime}}}$

Here, E′ represents the X-ray energy; S(E′) is the X-ray intensityspectrum emitted by the source that comes out of the belt in thescanner; D^(E)(E′) are the sensitivities of the dual-energy detectors toX-rays of energy E′. One representation of the material transmittancefunction is:

${T_{M}\left( {\rho_{M},t_{M},E^{\prime}} \right)} = {\exp \left\lbrack {{- \rho_{M}}t_{M}\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \right\rbrack}$

The transmittance function of the material is an inverse exponentialfunction of the product of the mass density ρ_(M), the path length t_(M)and the mass attenuation

$\frac{\mu}{\rho_{m}}$

of the material. The material transmittance is represented by T_(M) inthe above equation and the mass density of the material is representedby ρ_(M) in the above equation. The mass attenuation coefficient of amaterial is, according to the mixture rule, the weighted average of themass attenuation coefficients of the chemical elements composing thatmaterial. Therefore, one representation of the mixture rule may be:

${{\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} = {\sum\limits_{i\epsilon M}\; {w_{i}\frac{\mu}{\rho}\left( {Z_{i},E^{\prime}} \right)}}},$

where E′ represents the x-ray energy. The elements i in the material,represented by their atomic number Z_(i), are weighted by their weightfractions w_(i), or in other words, the product of the number of atomswith the atomic mass of each element divided by the total mass of themolecule of the material. Both the mass attenuation coefficient, whichmay be represented by

${\frac{\mu}{\rho}\left( {Z_{i},E^{\prime}} \right)},$

and atomic masses, which may be represented by A_(i), of variouselements are available in atomic databases.

From an X-ray point of view, a material is totally described by itsenergy-dependent attenuation cross section per mol of electron andelectron density because these two properties completely encapsulate thex-ray absorption properties of a material. Therefore, to have physicalmeaning, the effective atomic number, Z_(eff), must be defined byspecifying the attenuation cross section of a material with a givenZ_(eff). For an element i, with an atomic number Z_(i), this may berepresented as:

${{\sigma_{e}\left( {Z_{i},E^{\prime}} \right)} = {\frac{\mu}{\rho}\left( {Z_{i},E^{\prime}} \right)\frac{A_{i}}{Z_{i}}}},$

where σ_(e) is the energy-dependent attenuation cross section of anelement i with atomic number Z_(i). The energy-dependent attenuationcross section per mol of electron of an element is given by the productof the mass attenuation coefficient with the molar mass over the numberof electrons per (unionized) atom of that element, which also happens tobe the atomic number of that element.

Therefore, a first step to determining a Z_(eff)-dependent attenuationcross-section is to first determine an energy-dependent attenuationcross-section for a material M as shown in steps 338 and 340 for thefirst and second reference materials, respectively. In the context ofassigning effective atomic number values to the reference materials, thematerial M is one of the two reference materials. Accordingly, themethod described herein for assigning Z_(eff) values to x-ray signalenergy attenuation must be performed for each of the two referencematerials. The energy-dependent attenuation cross section for a materialM is given by the average of the energy-dependent attenuation crosssection per mol of electron of each element in that material, weightedby the total number of electrons of each element.

Then, the way to assign a Z_(eff) to a material that reproduces itscross section is to define a Z_(eff)-dependent cross section and to setthe Z_(eff) to the value that best fits the previously definedenergy-dependent attenuation cross section for a material M, as shown insteps 342 and 344 for each of the first and second reference materials,respectively. One suitable physics-based definition for theZ_(eff)-dependent cross section is a linear combination of the crosssections of the two elements Z_(i) and Z_(i+1) immediately adjacent tothe Z_(eff) value. This could be replaced by another model that fulfillsthe same purpose. However, if it is considered that the best Z_(eff)value is such that the Z_(eff)-dependent cross section is equivalent tothe energy-dependent attenuation cross section of a material, theeffective atomic numbers for each energy domain are fixed. In order todefine a single Z_(M) for material M, it is necessary to weight theenergy dependent curve of Z_(M) properly.

The evaluation of Z_(eff) is based on transmission measurements of apolychromatic X-ray spectrum emitted by the source through the materialof interest and other structural materials composing the scannerhousing. Thus, the weighting of the energy dependent Z_(eff) curve mustbe based on the transmission measurements of the incoming X-rayspectrum. The fraction of incoming X-ray of energy transmitted throughthe material, or simply the material transmittance, is an inverseexponential function of the electron density and the attenuation crosssection of material M. The electron density of material M is defined byits actual mass thickness and the weight fractions, atomic number andmass of each element that composes it. The mass thickness is defined asthe product of the mass density and the path length. An equivalentZ_(eff)-dependant material transmittance can be defined by using theZ_(eff)-dependent cross section instead of the energy-dependentattenuation cross-section, which closely resembles the actualenergy-dependent transmittance function of the material. This value isdetermined by minimizing the weighted squared transmission error, whichis given by integrating the weighted difference between the materialtransmission curve and the equivalent Z_(eff)-dependant materialtransmittance over the X-ray energy spectrum. Since the Z_(eff) isultimately determined using the total radiative energy transmittedthrough the material M and absorbed in the dual-energy detectors, theweighting is preferably a compromise between the dual-energy signalweighting, which complicates the error minimization procedure, butavoids ending up with two different Z_(eff) (one per energy level), andthe intensity spectrum weighting described in the publication K. Bond,J. Smith, J. Treuer, J. Azevedo, J. Kallman et H. Martz, «ZeCalcalgorithm details,» LLNL, Livermore, C A, 2013, which is hereinincorporated by reference in its entirety, that neglects the dependencyof Z_(eff) on the detection system.

Accordingly, the steps following the definition of the Z_(eff)-dependentcross-section for each energy level for each of the reference materialsinclude evaluating the energy-dependent material transmittance functionusing the previously defined energy-dependent attenuation cross-sectionfor each energy level, as shown in steps 346 and 348 for the first andsecond reference materials, respectively, and re-evaluating theenergy-dependent material transmittance function using theZ_(eff)-dependent cross-section as shown in steps 350 and 352 for eachof the first and second reference materials, respectively, to provide aZ_(eff)-dependent material transmittance function and a weighted squaredtransmission error as shown in steps 354 and 356. The weighted squaredtransmission error of the low-energy x-ray energy signal is thenminimized in steps 358 and 360 to assign a single Z_(eff) value to eachof the reference materials as shown in steps 362 and 364. It should beunderstood that the step of evaluating the energy-dependent materialtransmittance function using the previously defined energy-dependentattenuation cross-section for each energy level may be performed oncethe energy-dependent attenuation cross-section of each of the low-energyx-ray signal domain and the high-energy x-ray signal domain isdetermined.

It should be understood that the high-energy energy-spectrum-detectorweighting function or a combination of the low-energy and high-energyenergy-spectrum-detector weighting functions, could be used instead ofthe low-energy energy-spectrum-detector weighting function in order toprovide a single Z_(eff) value to be attributed to the high andlow-energy x-ray signal information provided by each of the tworeference materials.

The effective atomic number information may be stored in lookup tablesor in archive for use in other operations as in step 318 though this isnot necessarily required for the purposes of the method describedherein. This may avoid the need to execute this potentiallycomputationally intensive step in later operations wherein effectiveatomic number information may be used. Collectively, the effectiveatomic number values corresponding to a particular set of dual-energyattenuation images for the pair of reference materials may be referredto as the “effective atomic number images” or simply the “Z_(eff)images”.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Mass Thickness to Reference Material AttenuationInformation

The step 312 of mass thickness lookup table generation is discussed infurther detail with reference to FIG. 12. Once the path lengthinformation for the reference materials has been assigned to thedual-energy x-ray attenuation as in step 306, the path lengthinformation may be used as a basis for assigning mass thickness valuesto the dual-energy x-ray attenuation for each of the reference materialsas indicated in step 312. It should be noted that the determination ofmass thickness for the reference materials is not dependent on thedetermination of the Z_(eff) value for the reference materials in step312. Accordingly, the determination of mass thickness may be performedindependently of or in addition to the determination of Z_(eff) for thereference materials.

The dual-material decomposition approach includes rewriting the factorinside the aforementioned exponential function representing the materialtransmittance as a sum of two similar terms over the pair of referencematerials. So, the product of the mass thickness and the massattenuation of a material M is equivalent to the sum of the products ofthe mass density and mass attenuation coefficient of the first andsecond. The mass thickness of a material corresponds to the mass of thatmaterial by unit area seen by the detector. Since the source emitsX-rays radially, the area seen by the detector increases as the objectmoves toward the detector. This effect may be disregarded in the presentmethod. From a dual-material decomposition point-of-view, thedual-material mass thickness of a material M is defined as the sum ofthe mass thicknesses of the first and second reference materials.

In taking the above into consideration, the first step for assigningmass thickness values to the dual-energy x-ray attenuation informationincludes determining the mass density of each of the first and secondreference materials as shown in steps 366 and 368, respectively. Sincethe physical properties of each reference material are known, this stepmay, for example, be completed by retrieving the appropriate informationfrom a suitable source. The next step includes determining the first andsecond reference material equivalent path lengths. This may, forexample, be done prior to, subsequently to or in conjunction with steps366 and 368, using the method described above with reference to FIG. 3for assigning path length information to dual-energy attenuation valuesobtained by scanning each of the two reference materials as in step 306.The attenuation information may be imposed on an inverse attenuationsurface to identify the corresponding path lengths for each of the firstand second reference materials. Subsequently, a product of the firstmaterial equivalent path lengths and the mass density of the firstreference material is taken at step 370 to provide a first referencematerial mass thickness at step 372. Similarly, a product of the secondmaterial equivalent path lengths and the mass density of the secondreference material is taken at step 374 to provide a second referencematerial mass thickness at step 376. The first reference material massthickness and the second material mass thickness may then be summed atstep 378 to provide a total mass thickness of the first and secondreference materials at step 380.

As with the effective atomic number, the mass thickness valuesassociated with the dual-energy x-ray attenuation for each of thereference materials may be stored in lookup tables as in step 318 or inarchive for use in other operations, though this step is not requiredfor the purposes of the method as described herein. This may avoid theneed to execute this potentially computationally intensive step in lateroperations wherein mass thickness information may be used. Collectively,the mass thickness values corresponding to a particular set ofdual-energy attenuation images for the pair of reference materials maybe referred to as the “mass thickness images”.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Z_(eff) to Attenuation Information of Unknown Material

Once the effective atomic number Z_(m) of the two reference materialswith known atomic composition are known from step 316 and that the massthickness ρt_(M) has been defined as in step 314, these values and thedual-material equivalent path lengths t_(m) as determined in step 306may be used to determine the effective atomic number of a material Mwith an unknown composition. The reference material equivalent pathlengths, effective atomic numbers and mass thicknesses may be determineddirectly by way of new scans and determination according to the methodsdescribed above or may be retrieved from suitable lookup tables. This isfurther discussed with reference to FIG. 13.

If the mass thickness of a reference material that represents the dualmaterial composition of a material M is divided by the mass thickness ofthat material M, it is shown by involving the surface S of the detectorthat this is equivalent to the weight fraction of that basis material inthe dual material decomposition of the unknown material

$\frac{\rho_{m}t_{m}^{M}}{{\rho t}_{M}} = {\frac{S\; \rho_{m}t_{m}^{M}}{S{\sum\limits_{m}{\rho_{m}t_{m}^{M}}}} = {\frac{\rho_{m}\left( {t_{m}^{M}S} \right)}{\sum\limits_{m}{\rho_{m}\left( {t_{m}^{M}S} \right)}} = {\frac{\rho_{m}V_{m}^{M}}{\sum\limits_{m}{\rho_{m}V_{m}^{M}}} = {\frac{m_{m}^{M}}{\sum\limits_{m}m_{m}^{M}} = \omega_{m}^{M}}}}}$

where V_(m) ^(M) and m_(m) ^(M) are effective volume and mass of basismaterial m in material M, respectively. Substituting the massthicknesses by weight fractions in the mass attenuation coefficientequation of the dual material decomposition, it becomes clear that thisis analogous to the mixture rule presented earlier, but this time in thecontext of the dual material decomposition. In other words,

${\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \approx {{\left\lbrack \frac{\rho_{1}t_{1}^{M}}{{\rho t}_{M}} \right\rbrack \frac{\mu}{\rho_{1}}\left( E^{\prime} \right)} + {\left\lbrack \frac{\rho_{2}t_{2}^{M}}{{\rho t}_{M}} \right\rbrack \frac{\mu}{\rho_{2}}\left( E^{\prime} \right)}}$becomes${\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \approx {{\omega_{1}^{M}\frac{\mu}{\rho_{1}}\left( E^{\prime} \right)} + {\omega_{2}^{M}\frac{\mu}{\rho_{2}}\left( E^{\prime} \right)}}$

Taking the mixture rule into consideration, this is equivalent to saythat the material M is made of a combination of the basis materials,just as it was previously defined in the mixture rule as being composedof a combination of different chemical elements.

The Z_(eff) of various materials are not necessarily positive integervalues, like the atomic number of chemical elements. Instead, they maketake any positive real values. When the Z_(eff) of a material is equalto an integer value, the mass attenuation coefficient must be equal tothe mass attenuation coefficient of the element that has an atomicnumber equal to that integer value. The behaviour of the massattenuation coefficient for non-integer Z_(eff) is provided by theaforementioned model. Of note, when the Z_(eff) is equal to one of thetwo reference materials, it can be expected that the mass attenuationcoefficient is the same as the mass attenuation coefficient of thatreference material. When a material M is decomposed into referencematerials (from the dual material decomposition), it can be furtherassumed that the reference materials could be further decomposed intotheir chemical elements (since their chemical composition should be wellknown). This concept is used to determine the weight fraction of eachbasis element j of the first and second reference materials:

${\overset{\_}{\omega}}_{j}^{M} = \left\{ \begin{matrix}{{\sum\limits_{m}{\omega_{m}^{M}w_{j \in m}}},} & {{{if}\mspace{14mu} j\mspace{14mu} {is}\mspace{14mu} {present}\mspace{14mu} {in}\mspace{14mu} m} = {{1\mspace{14mu} {or}\mspace{14mu} m} = 2}} \\{0,} & {otherwise}\end{matrix} \right.$

This effective basis element weight fraction can be used to determinethe mass attenuation coefficient for the unknown material, just like itwas used for the reference materials.

Accordingly, the method for assigning an effective atomic number to anunknown material begins at step 1300 with the scanning of an unknownmaterial in an x-ray scanning device to obtain dual-energy x-rayattenuation information for the unknown material at step 1302. Thedual-energy x-ray attenuation information of the unknown material maythen be imposed to the inverted attenuation surface at step 1304, orreferenced using a suitable lookup table, to determine equivalent firstand second reference material path lengths through the unknown materialas shown in steps 1306 and 1308. It should be understood thatcorresponding first and second reference material equivalent pathlengths may be retrieved from suitable lookup tables as provided bysteps 308 and 310 of FIG. 3, if stored in archive subsequent to a priorcalibration method scanning operation. The first and second referencematerial mass thickness in the unknown material may then be determinedat steps 1310 and 1312, respectively, using the equivalent first andsecond reference material path lengths and known mass density of thefirst and second reference materials. A total mass thickness of theunknown object may be determined as in step 1314 based on a sum of themass thickness of each of the first and second reference materials inthe unknown material. As shown in step 1316, the unknown object totalmass thickness may be divided by the unknown object path lengths throughthe unknown object to provide the mass density of the unknown object atstep 1318.

In the next step 1320, a first weight fraction of each of the first andsecond reference materials in the unknown material may be determined. Asecond weight fraction of each basis element of each of the first andsecond reference materials in the unknown material is also determined atstep 1322. A mass attenuation coefficient for the unknown material isdetermined at step 1324, with a product of the effective weight fractionof each basis element of each of the first and second material in theunknown third material and the mass attenuation coefficient of thecorresponding element in the first and second materials. The methodfurther includes at step 1326 determining an attenuation cross sectionof the unknown object. This may be accomplished, for example, by usingthe respective known basic atomic properties such as the respectiveeffective atomic masses and atomic numbers and mass attenuationcoefficient for each of the first and second material.

Then a procedure similar to the one used to assign an effective atomicnumber to the reference materials is used for the unknown material.Following the determination of the mass attenuation coefficient for theunknown material at step 1326, this includes the steps of defining aZeff-dependent attenuation cross-section as shown in step 1328,evaluating the energy-dependent material transmittance function at step1330 using the previously defined energy-dependent attenuationcross-section for each energy level and re-evaluating theenergy-dependent material transmittance function at step 1332 using theZ_(eff)-dependent cross-section to provide at steps 1334 and 1336,respectively, a Z_(eff)-dependent material transmittance function and aweighted squared transmission error for each energy level. The weightedsquared transmission error of each energy level and preferably thelow-energy x-ray energy signal is then minimized at steps 1338 and 1340,respectively, to assign a single Z_(eff) value to the unknown materialat step 1342. It should be understood that, as with the aforementionedmethod as described within the context of assignment of effective atomicnumber values to the first and second reference materials, the step 1332of evaluating the energy-dependent material transmittance function usingthe previously defined energy-dependent attenuation cross-section foreach energy level may be performed once the energy-dependent attenuationcross-section of each of the low-energy x-ray signal domain and thehigh-energy x-ray signal domain is determined. Accordingly, steps 1332and 1328, wherein the Z_(eff)-dependent attenuation cross-section isdefined, are interchangeable.

Note that this procedure does not actually depend on Z_(m) for m=1,2,but rather on the decomposition of the fictitious material on adual-material element basis. Thus, the Z_(eff) is calculated with onlyone additional approximation than Z_(m), i.e.: the generalized massattenuation coefficient of fictitious material M can be represented by alinear combination of the basis elements j of which the first and secondreference material are actually made of. This method is a “multi-elementdual-material decomposition” for the effective atomic numbercalculation.

Alternatively, instead of repeating the above process every time a newmaterial is scanned, this procedure can also be done in advance for allpoints (I^(LE),I^(HE)) in the dual-energy signal mesh. This generates,point by point, the effective atomic number surfaceZ_(eff)(I^(LE),I^(HE)) and associated uncertainties. Also, if a reversemodel associating attenuations to path lengths was used, a new set ofcoefficients {right arrow over (f)}, associated with the effectiveatomic number, has to be derived from the model selected and thedefinition of the effective atomic number adopted. Then theZ_(eff)(I^(LE), I^(HE)) of the set of coefficients {right arrow over(f)} is saved in an effective atomic number database.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Background Removal Method

Reference material path length decomposition also allows for a set ofdual energy images or image archives to be transformed into a new set ofdual energy images or image archives with layers of materials removed.Depending on the shape and nature of the materials removed, this canlead to images where contrast between objects is enhanced, or whereobjects are completely removed from the image. This is done byappropriately subtracting the mass thickness of the material or objectto be removed from the mass thickness of the combined objects in thearchive. Usually, the object to be removed is in the background of theobject that is of main interest. Different methods are used to properlyevaluate the mass thickness of the background material or object,depending on its shape and whether prior knowledge of it is available.

In some instances, the background to be removed is already known to theX-ray scanner operators. In such cases, the background will have beenscanned previously and preferably, the dual-energy images are availablein archive. One example of a background object which may be known to anX-ray scanner operator and may have been previously scanned would be astandard x-ray screening tray. Preferably, the tray will have beenscanned in the x-ray scanning device in various positions andorientations to provide a plurality of dual-energy images of thescreening tray which would be available for subsequent operations fromarchive. In these cases, a particular method can be used to remove thebackground object from a newly scanned dual-energy image representingx-ray signal information of the background object and an object ofinterest at least partially overlapping with one another.

In accordance with one aspect, there is provided a method for assigningan attribute to an object of interest overlapping with a predeterminedbackground object as shown in FIG. 14. The method includes firstscanning the predetermined background object in a plurality of positionsand orientations within an x-ray scanning device at step 1400 to obtaina plurality of first dual-energy attenuation images at step 1402 eachhaving dual-energy attenuation information representing the scannedbackground object. This scanning step 1400 can be performed offline,prior to performing a scan including an object of interest. Then, thebackground object dual-energy attenuation images may then be decomposedinto background object dual-reference material equivalent path lengthimages having first and second reference material equivalent pathlengths passing through the background object at step 1404. Suchdecomposition may be performed, for example, using suitable lookuptables or by way of the method described above with reference to FIG. 3.Thereby, there is provided a reference material equivalent path lengthimages of the predetermined background object at step 1406.

In the next step 1408, the unknown object at least partially overlappingwith the background object may be scanned within the x-ray scanningdevice to obtain a second set of dual-energy attenuation images at step1410 each having dual-energy attenuation information representing anoverlap region wherein the background object and the unknown objectoverlap. Such an image is illustrated in FIG. 15, for example, whereinx-ray path lengths 1500 are shown passing through both the backgroundobject 1502 and the unknown object of interest 1504. Some of the x-raypath lengths pass through both of the background object 1502 and theunknown object of interest 1504 thereby creating an “overlap region”1506 within the image which overlap region is delineated by imaginarydashed lines 1508.

The second set of dual-energy attenuation images may then be decomposedat step 1412 into reference material equivalent path length imagesprovided at steps 1414, wherein the overlap region has first and secondreference material equivalent path lengths passing through both thebackground object and the unknown object. The position and orientationof the background object in the reference material equivalent pathlength images containing the overlap region is then determined at step1416, preferably by using a segmentation algorithm to localize thebackground object as shown in step 1418. It should be understood thatthe segmentation algorithm may be applied to either one of thedual-energy attenuation images or the reference material path lengthimages to localize the background object. Accordingly, the segmentationalgorithm may instead be applied to the images provided at step 1410, asshown in step 1430. Then, at step 1420, the position and orientation ofthe background object as identified by the segmentation algorithm iscompared with the reference material path length images of thepredetermined background object to determine corresponding ones of thereference material equivalent path length images of the predeterminedbackground object which most closely corresponds with the position andorientation of the background object in the reference materialequivalent path length images of the scanned unknown object with theoverlap region. Once this determination is made, the predeterminedbackground object reference material equivalent path lengths of thecorresponding ones of the plurality of the predetermined backgroundobject reference material equivalent path length images may beeliminated or subtracted from the overlap region in the referencematerial equivalent path length images of the unknown object at step1422 to provide reference material equivalent path lengths having firstand second reference material equivalent path lengths passing throughonly the unknown object, as shown in step 1424. There is therebyprovided background-free first reference material equivalent path lengthimages.

Decomposition of the dual-energy attenuation images of the predeterminedbackground object at step 1404 or the dual-energy attenuation imagesrepresenting the scanned unknown object at step 1412 into referencematerial equivalent path lengths may be performed in any mannerpreviously described, such as for example, by imposing the dual-energyattenuation information of each pixel onto the inverse attenuationsurface to obtain the first and second equivalent reference materialpath lengths or by using suitable lookup tables. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Once the background object-free reference material equivalent pathlength images are provided at step 1424, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1426, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1428. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

In another aspect, the background object to be removed is not known bythe operators but has or is determined to have a path lengthdistribution that is uniform. Preferably, the uniform path lengthdistribution is in the direction of the belt since in the image, thiscorresponds to the horizontal direction. Under such circumstances, asecond method may be used to effectively remove the background objectfrom the image. This method uses a region in the image where only thebackground object to be removed is present and there are no otherobjects or materials overlapping with the background object. Since thebackground is not known but has a uniform path length distribution,preferably in the horizontal direction, the background object must bethe same thickness in background only areas and in areas overlappingwith other objects. These conditions are understood to be true for eachrow of pixels in the image in which the background object must beremoved, since each row in the image corresponds to a different ray fromthe X-ray fan beam. To simplify, the background object path length isevaluated in a pixel in a background only region, and since, based onthe above conditions, it can be safely assumed to be the same in allother pixels of the same row of pixels, then the background object pathlengths can be removed, even if the background object itself is unknown.

There is provided a method as shown in FIG. 16 for assigning anattribute to an unknown object overlapping with an unknown backgroundobject having homogenous composition and thickness. In the first step1600, the unknown object at least partially overlapping with thebackground object is scanned within the x-ray scanning device to obtaina dual-energy attenuation images at step 1602 having pixels distributedin rows and columns and each having dual-energy attenuation information.The dual-energy attenuation images are then decomposed at step 1604 intodual-reference material equivalent path length images provided at step1606, each dual-reference material equivalent path length image having abackground region with first and reference material equivalent pathlengths passing through only the background object and an overlap regionwith first and second reference material equivalent path lengths passingthrough the unknown object of interest overlapping with the backgroundobject. The background region and the overlap region are then determinedat step 1608 by using a segmentation algorithm at step 1610 to localizethe background region within the dual-reference material path lengthimages of the unknown object. It should be understood that thesegmentation algorithm may be applied to either one of the dual-energyattenuation images or the reference material path length images tolocalize the background object. Accordingly, the segmentation algorithmmay instead be applied to the images provided at step 1602, as shown instep 1630. Then, at step 1612, one of an average, a median and a mean,preferably the average, of the first and second reference materialequivalent path lengths passing through only the background object ineach column is determined. At step 1614, the one of the average, themedian and the mean of the first and second reference materialequivalent path lengths passing through only the background object ineach column is eliminated or subtracted from the first second referencematerial equivalent path lengths of each column of the overlap region todetermine reference material equivalent path lengths representing onlythe unknown object of interest as shown at step 1616.

Once the background object-free reference material equivalent pathlength images are provided at step 1616, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1618, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1620. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

Even when no prior information about the background object is known andthe background object is not horizontally uniform, there is provided athird method to perform background object removal. Once again, themethod uses, in addition to regions of overlap of the background andanother object in the image, a region where there is only backgroundobject. The background object path lengths are known and may bedetermined using measurements or determined by way of a reconstructionalgorithm or any other suitable method. The mass density and averageatomic effective atomic number of the background object must be constantthroughout the background object, both in the background-only region andoverlap region of the image. Likewise, both the mass density andeffective atomic number of the reference materials from thedual-material decomposition must be known. Finally, the effective atomicmodel referred to earlier must be mathematically invertible.

In another aspect, there is therefor provided a method for assigning anattribute to an object of interest overlapping with a background objecthaving homogenous composition and non-uniform known thickness. In afirst step 1700, the unknown object at least partially overlapping withthe background object is scanned within the x-ray scanning device toobtain a dual-energy attenuation images at step 1702 each having pixelsdistributed in rows and columns and having dual-energy attenuationinformation. The dual-energy attenuation images are decomposed at step1704 into reference material equivalent path length images, provided atstep 1706, having a background region with first and second referencematerial equivalent path lengths passing through only the backgroundobject and an overlap region with first and second reference materialequivalent path lengths passing through the unknown object of interestoverlapping with the background object. The effective atomic number ofeach pixel of the dual-reference material equivalent path length imagesis determined at step 1708 and the mass thickness of each pixel of thebackground region and the overlap region in the dual-reference materialequivalent path length images is also determined at step 1710. In thenext step 1712, the background region and the overlap region arelocalized, preferably by using a segmentation algorithm as shown at step1714. It should be understood that the segmentation algorithm may beapplied to either one of the dual-energy attenuation images or thereference material path length images to localize the background object.Accordingly, the segmentation algorithm may instead be applied to theimages provided at step 1702, as shown in step 1740. Then, the pathlengths passing through the background object are obtained or determinedusing suitable methods at step 1716. The mass thickness of each pixel ofthe background region may be divided, as at step 1718 by the knownbackground object path lengths to determine the mass density of eachpixel of the background region as shown at step 1720. At step 1722, oneof an average, a median and a mean of the effective atomic number andthe mass density across all pixels of the background region isdetermined. At step 1724, for every pixel in the overlap region, themass density of the background region is multiplied with the pathlengths of the background region. Next, at step 1726, for every pixel inthe overlap region, the mass thickness of the background region iseliminated or subtracted from the total mass thickness of the backgroundregion and the overlap region to provide an unknown object massthickness at step 1728. Next, the density of the unknown object isdetermined. For every pixel in the overlap region, the unknown objectmass thickness is divided by the path length through the unknown objectto provide the density of the unknown object at step 1730. Once the massdensity is provided at step 1730, the effective atomic number of theobject is also calculated as shown at step 1732.

The effective atomic number of the object of interest is calculated byisolating the object effective atomic number in an equation that linksthe total mass thickness and effective atomic number values of everypixel with those of the object of interest and background object in theoverlap region:

g[Z _(eff)(i,j)]ρt(i,j)=g[Z _(o)]ρ_(o) t _(o)(i,j)+g[Z _(b)]ρ_(b) t_(b)(i,j)

where; Z is the effective atomic number of every pixel in the object andbackground in the overlap region, where g[Z] is an invertible functionof Z, where o and b represent the object and background respectively,where pt is the mass thickness, and where i and j represent the pixel ofthe j^(th) row and P column. Isolating the effective atomic number ofthe object Z_(o) gives:

${Z_{o}\left( {i,j} \right)} = {g^{- 1}{\left\{ \frac{{{g\left\lbrack {Z_{eff}\left( {i,j} \right)} \right\rbrack}{{\rho t}\left( {i,j} \right)}} - {{g\left\lbrack {\overset{\_}{Z}}_{b} \right\rbrack}{{\rho t}_{b \in {ob}}\left( {i,j} \right)}}}{{\rho t}_{o \in {ob}}\left( {i,j} \right)} \right\}.}}$

The background-free dual-material path lengths images of the object t₁^(o)(i,j) and t₂ ^(o)(ii) are then determined at step 1734 by solvingthe following system of equation for every pixel (i,j) in the overlapregion ob:

$\quad\left\{ \begin{matrix}{{{\rho t}_{o \in {ob}}\left( {i,j} \right)} = {{\rho_{1}{t_{1}^{o}\left( {i,j} \right)}} + {\rho_{2}{t_{2}^{o}\left( {i,j} \right)}}}} \\{{{g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack}{{\rho t}_{o \in {ob}}\left( {i,j} \right)}} = {{{g\left\lbrack Z_{1} \right\rbrack}\rho_{1}{t_{1}^{o}\left( {i,j} \right)}} + {{g\left\lbrack Z_{2} \right\rbrack}\rho_{2}{t_{2}^{o}\left( {i,j} \right)}}}}\end{matrix} \right.$

wherein the solutions are:

${t_{1}^{o}\left( {i,j} \right)} = {\frac{{\rho t}_{o \in {ob}}\left( {i,j} \right)}{\rho_{1}}\left\{ \frac{{g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}}{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}} \right\}}$${t_{2}^{o}\left( {i,j} \right)} = {\frac{{\rho t}_{o \in {ob}}\left( {i,j} \right)}{\rho_{2}}{\left\{ \frac{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack}}{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}} \right\}.}}$

Decomposition of the dual-energy attenuation images of the backgroundobject at step 1704 may be performed in any manner previously described,such as for example, by imposing the dual-energy attenuation informationof each pixel onto the inverse attenuation surface to obtain the firstand second equivalent reference material path lengths or by usingsuitable lookup tables. This is previously discussed with reference toFIGS. 3 and 11 and in particular step 306 shown in FIG. 11.

Once the background object-free reference material equivalent pathlength images are provided at step 1734, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1736, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1738. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Calibration Range Extension Method

The dual material decomposition described above in the calibrationmethod is best suited for the range of effective atomic numbers situatedbetween the effective atomic numbers of the reference materials used inthe calibration step wedges. It may be desirable to extend thecalibration range provided by a standard dual-material calibrationmethod while keeping the physical significance of inverse attenuationsurfaces generated using the calibration method. This would enabledual-material decomposition of a wider range of material compositionsthan would be possible for a given set of two reference materials with astandard dual-material calibration method.

In a first method, two or more of the ranges of the dual-material pathlength decomposition data may be combined to extend the total range ofdual-material path length decomposition data. In this first method,dual-material path length decomposition is performed on a firstreference material and a second reference material. Then, dual-materialpath length decomposition is performed on the second reference materialwith a third reference material. Therefore, the second referencematerial path attenuation information is common to both sets of data. Asubset of coefficients is then identified which may be used to combinethe dual-material decomposition information provided by the first andsecond reference material ({right arrow over (c)}₁₂ ^(E)) and the secondand third reference material ({right arrow over (c)}₂₃ ^(E)) based onthe common elements of the models used to represent the second referencematerial within the two data sets. Thereby, a broader range ofattributes may be assigned to x-ray attenuation values.

With reference to FIG. 18, in a first aspect, the method for assigningattributes to x-ray attenuation information includes as a first step1800 acquiring first and second reference material equivalent pathlength information associated with a first range of dual-energy x-rayattenuation information. At step 1802, second and third referencematerial equivalent path length information associated with a secondrange of dual-energy x-ray attenuation information is acquired. At step1804, suitable coefficients are determined for representing thedual-energy x-ray attenuation information of the second referencematerial. At step 1806, the coefficients are used to join the first andsecond dual-energy x-ray attenuation information ranges to define, atstep 1808, a third dual-energy x-ray attenuation information range uponwhich upon which may be imposed dual-energy x-ray attenuation valueswithin the third dual-energy x-ray attenuation information range todetermine corresponding first reference material equivalent path lengthsand third reference material equivalent path lengths.

The first and second reference material equivalent path lengthinformation and second and third reference material equivalent pathlength information may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at step 1810, having, respectively, saved first and second orsecond and third reference material equivalent path lengths associatedwith the dual-energy x-ray attenuation information corresponding withthe dual-energy attenuation information range. Alternatively, as shownat step 1812, the first and second or second and third referencematerial path length information may be determined by repeating thedual-material decomposition method previously described for fresh scansof suitable reference materials.

In another method, the calibration range may be extended using a singleadditional material. When decomposed onto the dual-material basis offirst and second reference materials, dual-energy attenuation curves ofthe second reference material may be represented by A₁₂ ^(E)(0, t₂;{right arrow over (c)}₁₂ ^(E)).

If it is further considered that a decomposition onto the dual-materialbasis of the first reference material and a third reference material,with the effective atomic number of the third reference material beinggreater than the effective atomic number of the second referencematerial and the effective atomic number of the second referencematerial being greater than the effective atomic number of the firstreference material, and the associated dual-energy direct attenuationsurfaces of the first and third reference material and correspondingcoefficients {right arrow over (c)}₃ ^(E) of the third referencematerial, then it is understood that the second reference material wouldbe represented by a subset of data in the range of the first referencematerial and the third reference material. This concept is illustratedin FIG. 19 wherein the range provided by the first reference materialand the third reference material is represented by the first quadrant ina graph. The second reference material is represented by a specificradial axis coming out of the origin in the first quadrant of the t₁-t₃plane. If the inverse attenuation surfaces for the first and thirdreference materials are available, then all the pixels of the first andthird reference material path length images of an object made of thesecond reference material would fall on this axis, no matter the pathlength through the second reference material.

Denoting the slope of the line supporting the axis representing thesecond reference material in the t₁-t₃ plane by ω₂, the line equationmay be represented by:

t ₃=ω₂ t ₁

The orientation of this line can also be defined by the volume fractionof the first reference material in the dual-material basis of the firstand third reference materials representing the second reference materialthis may be represented by:

$v_{2} = {\frac{1}{1 + \omega_{2}} = \frac{t_{1}}{t_{1} + t_{3}}}$

The sum of the first and third reference materials path lengths on theaxis representing the second reference material may be represented by:

s ₂ =t ₁ +t ₃

Since t₁, t₃≥0 in the first quadrant, s₂≥0 and s=0 if and only ift₁=t₃=0 (i.e. at origin) Then, the change of variables (t₁, t₃)→(s₂, v₂)can be defined using the set of equations:

$\quad\left\{ \begin{matrix}{{t_{1}\left( {s_{2},v_{2}} \right)} = {v_{2}s_{2}}} \\{{t_{3}\left( {s_{2},v_{2}} \right)} = {\left( {1 - v_{2}} \right)s_{2}}}\end{matrix} \right.$

The dual-energy attenuation curves over the axis representing the secondreference material in the dual-material basis provided by the first andthird reference materials may therefore be represented as

A₁₃ ^(E) (s₂, v₂; {right arrow over (c)}₁₃ ^(E)) for s≠0. For s=0, it isclear that attenuations vanish for both the high and low energy level.By the reunion of the domains (s₂=0 and s₂≠0), then A₁₃ ^(E) (s₂, v₂;{right arrow over (c)}₁₃ ^(E)) is defined over the domain s₂≥0.

For fixed v₂ and dual-energy attenuations that could be both achievedfor a given path length t₂ through the second reference material, itshould be understood that in general: t₂≠s₂. However, there is anonlinear path length-dependent scaling factor S₂(t₂) mapping locallyA₁₂ ^(E)(0, t₀; {right arrow over (c)}₁₂ ^(E)) onto A₁₃ ^(E)(s₀, v₂;{right arrow over (c)}₁₃ ^(E)) for some s₀=S₂(t₀). The union of all suchmappings along the axis representing the second reference material inthe dual-material decomposition of the first and third referencematerial plane leads to a continuous function s₂=S₂(t₂). Physically, wealso know that S₂(0)=0.

Therefore, in order to extend the calibration range provided by thedual-material decomposition of the first and second reference materialup to a calibration range provided by the dual-material decomposition ofthe first and third reference material without having to first determinethe direct or inverse attenuation surfaces of the dual-material basisprovided by the first and third reference materials, it is desired todetermine the map S₂ between t₂ and s₂, the dual-material basis providedby the first and third reference materials and the orientation v₂ of theaxis representing the second reference material in the first and thirdreference material dual-material basis.

It can be assumed that there is an orientation and a scaling factor suchthat:

A₁₂ ^(E)(0, t₂; {right arrow over (c)}₁₂ ^(E))=A₁₃ ^(E)(S₂(t₂), v₂;{right arrow over (c)}₁₃ ^(E)) all over the s₂ axis. Thus, using thisequivalence principle and knowing that A₁₂ ^(E)(0, t₂; {right arrow over(c)}₁₂ ^(E)) explicitly, the mapping S₂(t₂) can be found implicitly forfixed v₂. v₂ can be determined because the above equation holds truewhen t₂=s₂=0.

In accordance with the above and with reference to FIG. 20, a secondaspect of the method for assigning an attribute to x-ray attenuationincludes acquiring at step 2000, first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information by a first model forexpressing collectively each of the first reference material pathlengths and the second reference material path lengths as a function ofthe associated first range of dual-energy x-ray attenuation information.The first range of dual-energy attenuation information is fitted withthe first model by a first set of coefficients. At step 2002, the firstset of coefficients is determined. At step 2004, there is acquired thirdreference material equivalent path length information associated with asecond range of dual-energy x-ray attenuation information by a secondmodel for expressing collectively each of the third reference materialequivalent path lengths as a function of the associated second range ofdual-energy attenuation information. The second range of dual-energyattenuation information is fitted with the second model by a second setof coefficients. At step 2006, the second set of coefficients isdetermined. The third reference material has an effective atomic numbergreater than that of the second reference material. At step 2008, thefirst set of coefficients and the second set of coefficients arecombined to provide a third set of coefficients at step 2010 for fittingthe first and second range of dual-energy x-ray attenuation informationwith a third model for expressing collectively the first and thirdreference material path lengths as a function of the fitted first andsecond range of dual-energy x-ray attenuation information. For allpoints in the third model, there is determined at step 2012, a volumefraction of one of the first and the third reference material whichrepresents the second reference material path lengths to identify wherein the third model path lengths representing the second referencematerial are represented. There is thereby provided at step 2014 thethird dual-energy x-ray attenuation range.

The first and second reference material equivalent path lengthinformation and third reference material equivalent path lengthinformation may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at steps 2016 and 2018, having, respectively, saved first andsecond or third reference material equivalent path lengths associatedwith the dual-energy x-ray attenuation information corresponding withthe dual-energy attenuation information range. Alternatively, as shownat steps 2020 and 2022, the first and second or third reference materialpath length information may be determined by repeating the dual-materialdecomposition method previously described for fresh scans of suitablereference materials.

With reference to FIGS. 21 and 22, there is provided, in a third aspect,a method for extending the calibration range provided by a first andsecond reference material beyond the effective atomic number range ofthe reference materials. Direct attenuation surfaces fitted on thecalibration data for the first and second reference materialdual-material decomposition basis, shown in the first quadrant of FIG.22 are also valid in regions of the second and fourth quadrants near theaxis representing the first reference material path lengths (t₁-axis)and the second reference material path lengths (t₂-axis), respectively,This is equivalent to extending the first reference material pathlengths t₁ or the second reference material path lengths t₂ to slightlynegative values while the other remains positive. Negative path lengthsrepresent an imposed or fictitious amount of a reference material thatwould have to be added to the dual-material images of the scanned objectfor the effective atomic number of the composite object (original objectplus the added negative layer) to provide a reference material pathlength that would result in finding an effective atomic number equal tothat of the actual reference material.

However, in order to provide more accurate and useful data, thisextrapolation must be constrained to predetermined minimum and maximumeffective atomic numbers for the imposed materials making up thenegative path lengths. Preferably, this minimum effective atomic numberis approximately equal to or greater than 3 and the maximum effectiveatomic number is approximately equal to or less than 42.

In this third aspect, there is provided a method for assigning anattribute to x-ray attenuation. In a first step 2100, there is acquiredfirst and second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation by a model for expressing collectively each of the firstreference material path lengths and the second reference material pathlengths as a function of the associated first range of dual-energy x-rayattenuation information. At step 2102, an extrapolation range ofdual-energy x-ray attenuation information is selected over which firstand second reference material path lengths are to be associated withdual-energy x-ray attenuation information of a first imposed materialhaving a predetermined minimum effective atomic number less than aneffective atomic number of the first reference material and a secondimposed material having a predetermined maximum effective atomic numbergreater than an effective atomic number of the second referencematerial. The first range is within the extrapolation range. At step2104, a set of fitting constraints is selected for associating each ofthe first reference material path lengths and the second referencematerial path lengths over the extrapolation range of dual-energyattenuation information. At step 2106, the set of fitting constraintsare applied to the model to define at step 2108 extrapolated first andsecond reference material equivalent path lengths over the extrapolationrange.

The first and second reference material equivalent path lengthinformation may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at step 2110, having therein saved first and second referencematerial equivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the dual-energy attenuationinformation range. Alternatively, as shown at step 2112, the first andsecond reference material path length information may be determined byrepeating the dual-material decomposition method previously describedfor fresh scans of suitable reference materials.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Object Reconstruction Method

There is also provided a method to find the density and effective atomicnumber Z_(eff) of objects present in scanned images. This isparticularly useful in the context of identification of LAG(liquid-aerosol-gel) materials which may be contained within a containerat the time of scanning.

With reference to FIGS. 23A and 23B, in a first aspect, the method forassigning attributes to an object of interest may be described asfollows. However, it should be understood that certain steps in themethod may be performed by different means, depending on the conditionsrelating to the object of interest that is scanned without departingfrom the scope of the invention described herein. Certain steps may alsobe performed in a different order than that presented in the followingdescription.

In a first step 2300, the unknown object of interest is scanned.Typically, the object of interest at least partially overlaps with abackground object within an x-ray scanning device, such as, for example,a security screening tray. The unknown object may also be containedwithin a container that is placed within the tray for the scanningoperation. The x-ray scanning device emits x-rays from at least twosources which pass through the unknown object and the background objectto be detected by at least one array of detectors. The detectors provideat step 2302 a plurality of dual-energy attenuation images each havingdual-energy x-ray attenuation information representing the container andan overlap region wherein the background object, the container and theunknown object of interest overlap.

Next, at step 2304, the dual-energy attenuation images are decomposedinto reference material equivalent path length images, which areprovided at step 2306. At step 2308, the reference material equivalentpath lengths representing the background object are removed from thereference material equivalent path length images. This may be done, forexample, using the methods described above with respect to backgroundobject removal. Thereby, there is provided at step 2310 referencematerial equivalent path lengths representing the unknown object and thecontainer.

At step 2312, the reference material equivalent path lengthsrepresenting the unknown object are converted to unknown object pathlengths multiplied by a predetermined scaling factor. Such a conversionmay be accomplished, for example by applying the following function foreach of the first and second reference material equivalent path lengthsrepresenting the unknown object:

$\mspace{76mu} {{t_{o}\left( {i,j} \right)} = {\frac{{\rho t}_{ob}\left( {i,j} \right)}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}}$t_(o)^(*)(i, j) = ρt_(ob)(i, j)(g[Z_(ob)(i, j)] − g[Z_(b)]) × scaling  factor = t_(o)(i, j) × scaling  factor = t_(o)(i, j) × SF$\mspace{79mu} {{{With}\mspace{14mu} {SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}\mspace{14mu} {when}\mspace{14mu} {t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}}$

wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants. Next, at step2314, the effective atomic number for each pixel representing theunknown object and the container is determined.

At step 2316, the mass thickness for each pixel representing the unknownobject and the container is determined. The mass thickness is equivalentto the unknown object path lengths representing the unknown object ofinterest multiplied by the scaling factor. At step 2318, there isidentified each first source-detector pair line defined by a first x-rayextending between a first one of the at least two sources and onedetector of the array of detectors in a first one of the plurality ofdual-energy attenuation images on which lies one scaled unknown objectpath length. At step 2320, there is identified each secondsource-detector pair line defined by a second x-ray extending between asecond one of the at least two sources and one detector of the array ofdetectors in a second one of the plurality of dual-energy attenuationimages on which lies one other scaled unknown object path length, thesecond one of the plurality of dual-energy attenuation images havingbeen generated contemporaneously with the first one of the plurality ofdual-energy attenuation images.

At step 2322, the extremities of each of the scaled unknown object pathlengths are joined to provide a scaled contour of the unknown object atstep 2324. The contour of the unknown object of each of the first andthe second one of the plurality of dual-energy attenuation images arethen iteratively matched at step 2326 to reduce the scaling factor ofthe scaled unknown object path lengths representing the unknown objectand provide unknown object path lengths at step 2328 and thereby acontour of the unknown object at step 2330.

The contour of the unknown object is then defined as an inner contour ofthe container at step 2332. At step 2334, there are identified thirdsource-detector pair lines defined by third x-rays extending betweeneach source and one detector of the array which intersect with thecontainer at only one point of intersection in each of the first andsecond one of the plurality of dual-energy attenuation images. Thesethird source-detector pair lines delimit at step 2336 an outer bound ofthe container as the pixels within the third source-detector pair lines.At step 2338, the outer bound of the container extending between the onepoint of intersection of each third source-detector pair line isinterpolated to define an outer contour of the container at step 2340.At step 2342, path lengths are determined which represent the containeras path lengths which extend between the inner contour of the containerand the outer contour of the container. Next, at step 2344, an effectiveatomic number of the unknown object is determined and at step 2346, amass density of the unknown object is determined.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2304 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2348 or byusing suitable lookup tables as in step 2350. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

The step 2306 for removal of reference material equivalent path lengthsrepresenting the background object, such as a security screening tray,from the images may be performed in a number of ways depending on theproperties of the background object.

The first method for removal of background objects, shown in FIG. 24, isto first, at step 2400, scan predetermined background objects, such as,for example, empty trays at various locations on the scanner belt and invarying angles of rotation or orientation within the scanning chamber toprovide low and high energy x-ray signal images at step 2402. The lowand high energy x-ray signal information for each pixel in each of thescans of the tray, along with position and angle data of the tray, arestored in a database at step 2404. This is done, for example, bycontouring the tray image and tracing a rectangle around it with asegmentation algorithm, as shown at step 2406, and saving the measuredvalues of the image and the corresponding tray placement information ina database. Then, when an unknown object of interest is scanned at step2408 in a tray using the x-ray scanner to provide low and high energyx-ray signal images of the unknown object overlapping with the tray atstep 2410, the stored tray image that is closest in position and angleto that scanned with the unknown object of interest is found in thedatabase at step 2412, once again, for example, by tracing a rectanglearound the tray using a segmentation algorithm at step 2414 and thencomparing at step 2416 that rectangle to the positions and angles of thetray in the stored database tray images. The database tray image is thenregistered at step 2418 on the scanned image of the unknown object ofinterest, simply by rotating and translating it so the angle andposition are a closer match. Finally, the tray image low and high energysignals are subtracted from the scan image at step 2420 to providebackground-free low and high energy signals representing only theunknown object at step 2422.

The second method for removal of background objects is very similar tothe first method, except that in addition to saving the empty traysignal data, the reference material path lengths, from the calibrationmethod, are also saved. Once again this is done by contouring the trayimage and preferably tracing a rectangle around it with a segmentationalgorithm and saving the measured values of the image as well as thecalculated reference material path lengths and the corresponding trayplacement and orientation information in a database. Then, when anunknown object of interest is scanned in a tray in the x-ray scanningdevice, the stored tray image that is closest in position andorientation is found in the database. This is preferably done as in thefirst method by tracing a rectangle around the tray of the scanned imageand then comparing that rectangle to the stored database tray images'positions and angles. The database tray image is then registered on theobject scanned image, preferably by rotating and translating it so theangle and position are a closer match. Then, during the next step,instead of subtracting the tray image signals from the scanned trayimage as in the first method, the reference materials path lengths ofthe tray image are subtracted from the reference materials path lengthsof the scanned image. This second method is therefore in accordance withthe method for removal of background object path lengths discussed abovewith reference to FIG. 14.

The third method for removal of background objects from a scanned imageis to directly apply the procedure explained previously relating to theremoval of a background object with homogeneous composition andnon-uniform path length distribution. With this method, the tray pathlengths in the region of overlap of the background object or tray andobject of interest must be known, as well as the density and effectiveatomic number of the material the tray is made of, in order to calculatethe mass thickness of the tray to be removed from the mass thickness ofthe scan image. They can be calculated by first obtaining or creating a3D model of the tray. Then the position and rotation angle of the trayin the scanner must be determined. This can be done once again using asegmentation algorithm and preferably by tracing a rectangle around thetray in the scan image. The 3D model of the tray is then simulated inthe scanner geometry with the proper position and angle. A ray castingalgorithm may be used to find the path lengths through the tray forevery pixel. The ray casting algorithm can be executed by the graphicsprocessing unit (GPU) to speed up the process. If they have not beendetermined beforehand, the tray density and effective atomic number canbe obtained from the image by applying the dual-reference material pathlength decomposition method previously described. With both thesematerial properties and the tray path lengths, it is possible tocalculate the reference material path lengths for the whole tray. Thesereference material path lengths can then be subtracted from thereference material path lengths of the overlap region of the image,which results in the reference material path lengths of the imagewithout the tray. These reference material path lengths can then be usedto calculate the signal, attenuation, mass density and effective atomicnumber for the image without the tray.

With reference to FIG. 25, the third method for removal of backgroundobjects begins with the step 2500 of scanning a predetermined backgroundobject to provide low and high energy x-ray signal images at step 2502.At step 2504 there is obtained a three-dimensional model of thebackground object according to the position and orientation of thebackground object as scanned in the x-ray scanning device. At step 2506,the reference material equivalent path lengths through the backgroundobject in the three-dimensional model are determined for each pixelusing a ray casting algorithm as shown at step 2508 or any othersuitable reference material decomposition means as previously described.The effective atomic number of each pixel the background object isdetermined at step 2510 and the mass density of each pixel of thebackground object is determined at step 2512. Next, at step 2514, themass thickness of the background object is determined by multiplying thepredetermined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject. At step 2516, the background object and overlap region arelocalized in the dual-reference material equivalent path length imagesof the unknown object scanned with the background object, preferablyusing a segmentation algorithm as shown at step 2518. At step 2520, themass thickness of the background object is eliminated from the massthickness of the reference material path length images to obtain a massthickness of the unknown object at step 2522. The first and secondreference material equivalent path lengths through the unknown objectare thereby provided at step 2524.

A preferred next step in the method described in FIGS. 23A and 23B is todetermine the effective atomic number (Z_(eff)) of the container asshown at step 2352, if the container is present. The calibration methoddescribed above transforms the signal obtained for each pixel of thescanned image into mass thickness and Z_(eff) values. If the X-raycorresponding to a pixel has traversed multiple different materials, theresulting mass thickness and Z_(eff) are combinations (sum and weightedaverage) of the properties of those materials. In order to find theeffective atomic number of the container, a pixel of an X-ray thattraverses the container but not the object of interest must be observed.This can happen two possible ways: observation of a pixel representingthe “side” of the container in the scanned image, and, observation of apixel representing the “top” (whichever side is up) of the container,where there is no object of interest at that portion of the containerbecause of gravity. In these locations, the Z_(eff) of the container canbe directly obtained from the calibration method. The Z_(eff) valuesassociated with each pixel may be found, for example, by applying asegmentation procedure to the scan image, and then calculating theaverage (or another relevant statistical quantity) effective atomicnumber over the region of the container. If there is no container, ormore specifically the object of interest is not contained within acontainer, the mass thickness of each pixel, obtained from the abovedescribed calibration method, is equivalent to the object of interestdensity multiplied by the object of interest path length for that pixel.In that case, the density, which is unknown but constant across allpixels, acts as a scaling factor. Therefore, the mass thickness is ascaled version of the path lengths. If there is a container, then theprocedure explained above with reference to FIGS. 17A and 17B inrelation to the removal of a background object with a homogenouscomposition and non-uniform path length distribution may be used toevaluate the mass thickness of a material in the calibration method ifthe mass thickness and effective atomic number from the combination ofboth materials, as well as both of the materials' individual effectiveatomic numbers are known. This is true for the reference materials ofthe calibration method, but is also true for the container and object ofinterest materials:

${\rho_{o}{t_{o}\left( {i,j} \right)}} = {\rho \; {t_{ob}\left( {i,j} \right)}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}$${\rho_{b}{t_{b}\left( {i,j} \right)}} = {\rho \; {t_{ob}\left( {i,j} \right)}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{o} \right\rbrack}}{{g\left\lbrack Z_{b} \right\rbrack} - {g\left\lbrack Z_{o} \right\rbrack}} \right\}}$

where (i,j) is the pixel coordinates in the image, pt is the massthickness, g(Z) the effective atomic number model, the indices “o”stands for “object of interest”, “b” for background or bottle(container), “ob” for object of interest+background. ρt_(ob)(p) andg[Z_(ob)(i,j)] are obtained directly from the above describedcalibration method and g[Z_(b)] was obtained during the last step.

However, since the Z_(eff) and mass thickness are a combination of theunderlying materials and because of the nature of the objects beingscanned (object of interest within a container), there are no pixelsrepresenting only the object of interest. Also, there is no way ofapplying the layer removal procedure to the container without eitherhaving either the exact 3D model of the container or some pixels withonly container information and knowledge of the path length of thex-rays through the container in those pixels. Neither of these pieces ofinformation are available and g[Z_(o)] remains unknown. Therefore, themass thickness of the object of interest or container cannot beevaluated directly. However, values for the path lengths through theobject of interest multiplied by a constant, called a scaling factor,may still be determined from the previous equations, by estimating valuefor g[Z_(o)]. The result is a value that represents the path lengthsmultiplied by a constant, called scaling factor. Although the scalingfactor is unknown, it is the same for all pixels, which is sufficientfor this step of the procedure. Also, as explained previously, inparticular with respect to the aforementioned procedure for removal of abackground object having homogenous composition and horizontally uniformpath length distribution, the uncertainties for all formulations ((t₁,t₂) or (ρt, Z)) of the input values are known. It is therefore possibleto evaluate uncertainty, on the object of interest path lengthsdetermined with the present method. This information may be used toaffect the results in the subsequent steps.

Mass thickness is already equivalent to the path lengths multiplied byan unknown constant (the density). As it was explained previously,multiplying the path lengths by an arbitrary constant, still results inthe path lengths multiplied by an unknown constant called the scalingfactor. This step is about transforming a set of separate path lengthsinto a cohesive object of interest shape and eliminating the scalingfactor to find the real path lengths.

For a given scaling factor, the initial data set is composed of pathlengths for each pixel, for all images generated by each source, or inother words the length of the intersection for each X-ray and the objectof interest. Each detector-source pair is represented as a known linethrough space on which the corresponding path length through the objectof interest is located. Since the exact shape and location of the objectof interest is unknown, the position of the path length line segmentalong its supporting line is also unknown. However, all source-detectorsassemblies view the same object. Therefore, the contour of the object ofinterest in a given slice, created by joining the extremities of eachpath length with the extremities of its nearest neighbors, should be thesame in both views. Moving a path length along its supporting linemodifies the object of interest contour in two points, since its linemust both “enter” and “exit” the object of interest. The goal of thisstep is to move the path lengths so that the contours formed from everyview's path lengths are as similar as possible. Such movement may beaccording to pre-specified rules and constraints. Thereby, the contoursmay be superimposed in space and iteratively moved towards each other,since, if the contours found in two contemporaneous images generated bytwo different sources circumscribe the same space, then it means thatthe two contours are very similar. However, if the path lengths are toolong, it may be difficult to obtain such a result.

This process is similar to non-rigid point set registration, but wherethe different sets of points are being registered on each other, so allsets of points act as both the “source” and “target” at the same time.Accordingly, the conventional registration metrics are generalized totake that into account. Therefore, it can be divided into two mainsteps.

First, the distance between the sets of data representing the contour inboth images is measured in some way. This may be done either for eachpoint in each set (with particular attention spent on the fact that theamount for each set is different) or for the set as a whole or both.

Second, the points of each set are displaced to reduce the distancemeasured in the previous step. The points in each set can be displacedindividually, as a whole or both. However, contrary to regularregistration procedures, the points can only be moved parallel on theirsupporting lines, which means the displacement cannot only be acombination of translation and rotation of the whole set of points.Therefore, the points must be at least displaced individually.

The above two steps may be repeated until the desired level of “match”is attained. This can be defined either by a threshold on the distancemeasured in step one or the displacement of step two. The procedure canalso be stopped after a certain number of iterations has been reached.

This procedure can be repeated separately for each column in the image,also called a “slice”. A slice is the corresponding columns in the imageof each view acquired at the same time from the beginning of the scan ofthe object. Since the different sources irradiated parallel planes andthe belt moves at constant speed, the length of the container in everyimage is the same. The subdivision of the container lengthwisecorresponds to the pixel columns in the image, and is determined by thebelt speed and integration time of the electronic acquisition system,which is the same for both views. Therefore, each column in one viewcorresponds to another column in the other view that sees the samesection of the container, or the same “slice”, up to the spatialresolution of the detection system.

However, it is possible that this first scaling factor may not becorrect or optimal. The contour matching procedure is started at thelargest possible scaling factor then repeated for increasingly smallerscaling factors. This repetition is stopped when the contours attain thebest “level of match” compared to other scaling factors. By iterativelychoosing a scaling factor that is closer to the correct one, the “levelof match” should increase. When the “level of match” starts decreasing,this means that the scaling factor is moving further from the correctvalue, which makes it possible to evaluate the correct scaling factor.This procedure may be performed for several slices together orseparately.

In a next step, the container is reconstructed which in turn includesthe determination of the bounding box of the container and a bubble, ifpresent.

A bounding box is a set of lines that limits the area where the pathlengths must be contained and is defined by the edge pixels from allviews. The container bounding box is made of lines intersecting eachother. Since these lines are considered continuous in space, they do notinitially limit the permitted space to a polygon, as they should. Forthe object of interest, this is avoided by defining the bounding pointsfor each source-detector supporting line supporting each scaled pathlength, and the points defining the object of interest must be inbetween those bounding points. This procedure does not provide asuitable bounding box for the container, since the container points thatwill be created will not be necessarily be on the supporting lines.Therefore, the actual bounding polygon for the container must bedefined. This is done by finding all the bounding lines intersectionsand eliminating all points that are too far from the previouslymentioned bounding points. The bounding polygon is then simply the linejoining together all the points left. Also, when three bounding linesintersect at the same point, they usually appear as three intersections.In that case, the middle intersection is eliminated from the polygon.This creates a very small segment instead of a 3-way intersection point.This very small segment will be useful in further steps.

In a next step, the presence of an empty part inside the container, alsocalled a bubble, is detected when present, either by comparing theestimated thickness of the container under and above the container or byother means. The points composing the top surface of the object ofinterest are also determined.

The container path lengths are determined differently than the pathlengths for the object of interest. First, a model or contour must becreated for the container, which is done by “anisotropic scaling” of theobject of interest, so it touches the container bounding box. There areas many contact points of the scaled object of interest contour as thereare bounding box polygon sides. This can be done by applying fivehypotheses that can be relatively safely assumed about the container, inaddition to the previous rules and constraints that were used for theobject of interest reconstruction. First, for any path length that doesnot extend into an empty part of the container, the object of interestinside touches the container at both entry and exit points of object ofinterest path lengths. Second, the container must touch each side of thecontainer bounding box in at least one location. Third, although thecontainer thickness will generally not be constant, it should be asmooth function in between points of contact with the bounding box. Thiscan be achieved by interpolating the thickness between points ofcontact. Fourth, the point of contact on the bounding box is likely tobe either the one closest to the object of interest, or the one that isencountered when travelling along the normal of the object of interesttop surface. Fifth, if a bubble was detected and the part of the objectof interest that was closest to the bounding box is part of the topsurface of the object of interest, this side of the bounding box shouldnot be considered, since the exact point where the container is incontact with the bounding box is difficult to determine based on theobject of interest.

The first hypothesis allows for the creation of the inner contour of thecontainer, which is simply equal to the contour of the object ofinterest. The four subsequent hypotheses allow the creation of the outercontour of the container. To create a contour, whether inner or outer,corresponding model points are linked in the same order as the object ofinterest contour points. Container path lengths are then obtained byintersecting the supporting lines with that shape using, for example, aray casting algorithm. If the intersection would be outside the boundingbox, the intersection with the bounding box is used instead for thatpath length. Finally, the container contour is created by joining theextremities of these path lengths, as for the object of interestcontour.

If the container is too thin, the bounding box of the liquid (object ofinterest) may be the same as the bounding box of the container. In thatcase, the “anisotropic scaling” method is not optimal. The preferredalternative is to suppose instead that the container thickness isconstant. This thickness may be a preset constant, may be inferred fromthe geometrical transverse distance between adjacent pixels, or may beestimated from the Zeff of the container or by other means.

If a bubble is present in the container, then the container model may beerroneous, and a different model would be preferred. One such model useseither reflection or rotational symmetry to create the container,depending on the previously determined number of corners. Indeed,containers with an even number of corners (and sides) are more likely tohave vertical symmetry, whereas it is impossible for a container with anodd number of corners/sides to possess “vertical” symmetry if it has aside lying flat on the tray surface. Note here that vertical refers tothe axis that is normal to the tray surface on which the container islying.

Reflection symmetry can be useful if the top part of the container ispoorly defined but the bottom part is well defined, and the container issuspected to be vertically symmetrical. In such circumstances, anadditional procedure is used to modify the container model whichdifferentiates points that are part of the object of interest/bubbleinterface and points that are part of the object of interest/containerinterface. The latter, as well as the container points, are reflectedbased on an axis that is parallel to the tray surface. The reflectedcontainer points must also be tangential to the bounding box. Finally,points left under the reflection axis are eliminated, and sections ofcontour missing are interpolated.

Another way to determine the thickness of the container all around theobject of interest contour, is to first evaluate the thickness accordingto the previously detailed model. Then the periodicity of the containerthickness and/or object of interest radial size is evaluated. If it isdetermined to have a clear period, then the thickness can be taken fromone period and then repeated for the other periods.

This can be particularly useful if there are few contact points and thereal container thickness shifts in a way that is nonlinear in betweenthose points. In that case it is possible that the container contourunder the object of interest is more accurately defined because of theproximity with the bounding box. This case can be detected if the normalcontainer model leads to a container thickness over the object ofinterest that is much larger than the one underneath it.

In that case, the periodicity of the object of interest or containershape may be evaluated, either by performing a fast Fourier transform onthe radial size of the object of interest or by other means. If theshape is found to be periodic or if a bubble has been detected, then aspreviously indicated, the period is evaluated and the container contours(both inner and outer) are taken over a period and repeatedly rotatedaround the most likely centroid of the container to form a completecontour. The most likely segment of contour to be estimated correctly isthe one located directly under the container centroid, between thebounding box surface and the liquid.

Solution by pairs provides a second method of determining the thicknessof the container around the object of interest. The solution by pairscorresponds to solving the two base equations (individually):

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k)

for pairs of path lengths, transforming a situation of 2 equations-3unknowns for a single path length, to 4 equations-3 unknowns.

All possible pairs of pixels i can be used, as long as its supportingline sees both the object of interest and the container, even if theybelong to different slices j and views k. Pairs of resulting values thatare outside the range of possible values can be eliminated outright, andare most likely caused by an incorrect path length. Each pair will givea different value for ρ_(o), ρ_(b) and Z_(o), and so this method resultsin a distribution of values. The best value for each quantity isevaluated from descriptive statistics of the associated distribution. Itcan be also relatively safely assumed that the lower the spread of thedistribution, the more optimal the solution is likely to be.

There is provided a third method for determining the thickness of thecontainer wall whereby analytical functions may be fit on the data. Thismay be done in two different ways, for both of the base equationsreferred to in the above description for the solution by pairs. All fitsare made using quantities for all pixels i, slices j and views k.

The first fitting option is a linear fit on the following equations:

$\frac{{\rho t}_{ob}\left( {i,j,k} \right)}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}}$$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}{{\rho t}_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$

and the predictor

$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$

By fitting a linear regression, the slope of the first equation is ρ_(o)and the slope of the second equation is g[Z_(o)]ρ_(o). The intersect inthe first equation gives ρ_(b). Note that for both equations, o and bcan be switched interchangeably to instead find the container density asthe slope and object of interest density as the intersection. However,this has limited use since at this point the properties of the object ofinterest may be calculated without having to find the container density.

The second fitting option is to consider the base equations as bivariatelinear functions:

ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k), and the predictorρt_(ob)(i,j,k)

g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k),

-   -   and the predictor g[Z_(ob)(i,j,k)]ρt_(ob)(i,j,k)        For the first equation, the slope in direction x at y=0 is ρ_(o)        and the slope in direction y at x=0 is ρ_(b). For the second        equation, the slope in direction x at y=0 is g[Z_(o)]ρ_(o) and        the slope in direction y at x=0 is g[Z_(b)]ρ_(b).

Finally, g[Z_(o)] can be obtained by dividing g[Z_(o)]ρ_(o) by thepreviously obtained ρ_(o), and Z_(o) can be obtained with g⁻¹{g[Z_(o)]}.

It should be understood that the object of interest may not necessarilybe contained within a container. Under such circumstances, the methodmay proceed as follows with a number of steps being similar or identicalto those found within the method wherein the object of interest iscontained within a container, however, wherein determination of thecontainer characteristics and bounding box is not required.

With reference to FIG. 26, the method for assigning attributes to anobject of interest in another aspect may be described as follows.However, it should be understood that certain steps in the method may beperformed by different means, depending on the conditions relating tothe object of interest that is scanned without departing from the scopeof the invention described herein. Certain steps may also be performedin a different order than that presented in the following description.

In a first step 2600, the unknown object of interest is scanned.Typically, the object of interest at least partially overlaps with abackground object within an x-ray scanning device, such as, for example,a security screening tray. The x-ray scanning device emits x-rays fromat least two sources which pass through the unknown object and thebackground object to be detected by at least one array of detectors. Thedetectors provide at step 2602 a plurality of dual-energy attenuationimages each having dual-energy x-ray attenuation informationrepresenting an overlap region wherein the background object and theunknown object of interest overlap.

Next, at step 2604, the dual-energy attenuation images are decomposedinto reference material equivalent path length images, which areprovided at step 2606. At step 2608, the reference material equivalentpath lengths representing the background object are removed from thereference material equivalent path length images. This may be done, forexample, using any of the methods described above with respect tobackground object removal. Thereby, there is provided at step 2610reference material equivalent path lengths representing the unknownobject.

At step 2612, the reference material equivalent path lengthsrepresenting the unknown object are converted to unknown object pathlengths multiplied by a predetermined scaling factor.

At step 2614, the mass thickness for each pixel representing the unknownobject is determined. The mass thickness is equivalent to the unknownobject path lengths representing the unknown object of interestmultiplied by the scaling factor. At step 2616, there is identified eachfirst source-detector pair line defined by a first x-ray extendingbetween a first one of the at least two sources and one detector of thearray of detectors in a first one of the plurality of dual-energyattenuation images on which lies one scaled unknown object path length.At step 2618, there is identified each second source-detector pair linedefined by a second x-ray extending between a second one of the at leasttwo sources and one detector of the array of detectors in a second oneof the plurality of dual-energy attenuation images on which lies oneother scaled unknown object path length, the second one of the pluralityof dual-energy attenuation images having been generatedcontemporaneously with the first one of the plurality of dual-energyattenuation images.

At step 2620, the extremities of each of the scaled unknown object pathlengths are joined to provide a scaled contour of the unknown object atstep 2622. The contour of the unknown object of each of the first andthe second one of the plurality of dual-energy attenuation images arethen iteratively matched at step 2624 to reduce the scaling factor ofthe scaled unknown object path lengths representing the unknown objectand provide unknown object path lengths at step 2626 and thereby acontour of the unknown object at step 2628. Next, at step 2630, aneffective atomic number of the unknown object is determined and at step2632, a mass density of the unknown object is determined.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2604 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2634 or byusing suitable lookup tables as in step 2636. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Since multiple values have been obtained for the object of interestproperties, the values must be combined to provide a final best valueaccording to a set of criteria based on various evaluable metrics. Thedisparity, uncertainties of the values as well as the uncertainty on thescaling factor determined in relation to the contour of the object ofinterest, and various metrics determined by these can all be consideredin determining the final values, as well as their uncertainties. Theseuncertainties may be relied upon in the next step, the threatdetermination method.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Threat Determination Method

The purpose of the threat determination method is to calculate a threatmetric value and a safe metric value by comparing the Z_(eff) anddensity ranges of the object of interest, determined by way of themethods defined previously, to threat and safe maps built by scanningactual explosives and safe objects. A decision is made based on thesevalues and if a threat is detected, it is shown on screen for viewing bysecurity screening personnel or an alert condition is raised.

The density and Z_(eff) values of objects considered to be threats andsafe are used to build the maps. These can be acquired either by lookingin literature, making measurements, calculating properties from thechemical composition, using the calibration method presented above orusing scans and the method for object reconstruction described above, ora combination of these methods. The density/effective atomic numberjoint distribution depends on the source of the value or the method usedfor its acquisition. Then for each point of the whole domain of possibleobject density and Z_(eff) values (wherein the distribution is such thatdensity is on one axis and Z_(eff) is on the other axis), theprobability density of each known object of the corresponding map issuperimposed. So, for the pair (density, Z_(eff)), the probability forOBJECT 1 to have one specific (density, Zeff) is added to the map, theprobability of OBJECT 2 to have one specific (density, Zeff) is added tothe map, etc., until all objects for that category (safe or threat) havebeen added to the map. This is done for all possible (density, Z_(eff))pairs of the density and Z_(eff) domain. Each map is then normalized forthe number of objects it contains. The map therefore returns, for aspecific (density, Z_(eff)) pair, both “threat” and “safe” values thatare similar to a probability, that each represent how likely it is forthat pair to be a threat and a safe object.

Note that this step can be performed by using a suitable density/Z_(eff)mesh and by calculating the safe and threat metrics for each cell of themesh, or analytically by considering the sum of probabilities densitiesfor each object as continuous functions over the domain. An example of aprobability density for an object could be a binormal distributioncentered on the average density and Z_(eff) of that object. Thenormalized sum of all the distributions of the objects of one category,“safe” of “threat” are respectively called the safe map and threat map.

When an unknown object is scanned, a similar distribution is determinedfor that object as a result of the object reconstruction method,described above. This is called the value distribution.

The threat and safe metrics are simply the sum of the value distribution(assumed once again as a normal distribution) multiplied by eachcorresponding map, over the whole map:

${{Safe}\mspace{14mu} {metric}} = {\sum\limits_{i}{{safe}\mspace{14mu} {map}\mspace{14mu} \left( {\rho_{i},Z_{{eff},i}} \right)*{value}\mspace{14mu} {distribution}\mspace{14mu} \left( {\rho_{i},Z_{{eff},i}} \right)}}$${{Threat}\mspace{14mu} {metric}} = {\sum\limits_{i}{{threat}\mspace{14mu} {map}\mspace{14mu} \left( {\rho_{i},Z_{{eff},i}} \right)*{value}\mspace{14mu} {distribution}\mspace{14mu} \left( {\rho_{i},Z_{{eff},i}} \right)}}$

Here, the index i refers to each cell of the map, and ρ_(i), Z_(eff,i)represent the mass density and Z_(eff) for each of those cells.

For example, for the first cell, the safe metric value will be the“safe” value previously defined for the mass density and Z_(eff) of thatfirst cell, multiplied by the probability that the unknown object hasthat mass density and Z_(eff). This is repeated for each cell, and theresults are added together to provide the safe metric. This is done onceagain but with the threat map to provide the threat metric.

Or, if the maps are analytical,

${{Safe}\mspace{14mu} {metric}} = {\overset{\infty}{\underset{- \infty}{\int\int}}\mspace{14mu} {safe}\mspace{14mu} {map}\mspace{14mu} \left( {\rho,Z_{eff}} \right)*{value}\mspace{14mu} {distribution}\mspace{14mu} \left( {\rho,Z_{eff}} \right)d\; \rho \; d\; Z_{eff}}$${{Threat}\mspace{14mu} {metric}} = {\overset{\infty}{\underset{- \infty}{\int\int}}\mspace{14mu} {threat}\mspace{14mu} {map}\mspace{14mu} \left( {\rho,Z_{eff}} \right)*{value}\mspace{14mu} {distribution}\mspace{14mu} \left( {\rho,Z_{eff}} \right)d\; \rho \; d\; Z_{eff}}$

If the unknown object of interest has been determined to have propertiesthat are similar to a region of the map with a higher concentration ofpossible safe/threat mapped objects, then it will appropriately havecorresponding higher safe/threat metrics.

The threat metric is divided by or otherwise mathematically combinedwith the safe metric to give the threat ratio, and if the threat ratiois over the decision threshold, then the unknown object is a threat. Thethreshold is selected to maximize detection and minimize falsepositives, and its concept is thoroughly studied in decision theory. Itcan also be experimentally determined by scanning objects in differentconfigurations, conditions, containers, and evaluating the resultingsafe and threat metrics. The adjustment of the threshold then results ina number of safe and threat assessments, therefore resulting in aproportion of false positives and detection rates. It is then fixed toresult in the optimal proportion for the decision objectives dictated byexternal authorities and is dependent on the overall solution.

If the unknown objects or objects of interest are determined to bethreats, the pixels they occupy in the images are sent to the GUI partof the software for highlighting and user warning. An alert conditionmay also be raised.

With reference to FIG. 27, there is provided a method for assigning oneof a safe condition and a threat condition to an unknown object. Themethod begins with the step 2700 of determining a density value and aneffective atomic number value for a plurality of predetermined safeobjects and a plurality of predetermined threat objects. At step 2702,the density value and effective atomic number values of each of thepredetermined safe objects and predetermined threat objects are plottedin a probability map to correlate corresponding pairs of density valuesand effective atomic number values with each of the predetermined safeobjects and predetermined threat objects.

At step 2704 an unknown object is scanned to provide a plurality ofdual-energy attenuation images at step 2706 each having dual-energyattenuation information representing the unknown object. At step 2708,each of the dual-energy attenuation images are decomposed intodual-reference material equivalent path length images representing theunknown object, provided at step 2710. The reference material equivalentpath lengths representing the unknown object are converted at step 2712into unknown object path lengths multiplied by a predetermined scalingfactor.

At step 2714, the effective atomic number for each pixel representingthe unknown object is determined. At step 2716, the effective atomicnumber of the unknown object is imposed on the probability map todetermine a probability that the unknown object is correlated with oneof a predetermined safe object or a predetermined threat object,provided at step 2718. As a further optional step, an alert may beraised at step 2720 based on this probability. Such an alert may, bynon-exhaustive example, be an audible alert, a modification to thedisplayed image, or notification to the appropriate personnel, amongother suitable alert conditions.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2710 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2722 or byusing suitable lookup tables as in step 2724. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Moreover, in cases wherein removal of a background object orreconstruction of an object may be required, such removal of thebackground object and/or reconstruction may be performed accordingly toany suitable method previously described.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

While the invention has been described in terms of specific embodiments,it is apparent that other forms could be adopted by one skilled in theart. For example, the methods described herein could be performed in amanner which differs from the embodiments described herein. The steps ofeach method could be performed using similar steps or steps producingthe same result but which are not necessarily equivalent to the stepsdescribed herein. Some steps may also be performed in different order toobtain the same result. Similarly, the apparatuses and systems describedherein could differ in appearance and construction from the embodimentsdescribed herein, the functions of each component of the apparatus couldbe performed by components of different construction but capable of asimilar though not necessarily equivalent function, and appropriatematerials could be substituted for those noted. Accordingly, it shouldbe understood that the invention is not limited to the specificembodiments described herein. It should also be understood that thephraseology and terminology employed above are for the purpose ofdisclosing the illustrated embodiments, and do not necessarily serve aslimitations to the scope of the invention.

What is claimed is:
 1. A method for assigning attributes to an unknownobject comprising: scanning the unknown object within a container and atleast partially overlapping with a background object within an x-rayscanning device, the x-ray scanning device emitting x-rays from at leasttwo sources which pass through the object of interest and the backgroundobject, the x-rays being detected by at least one array of detectors toprovide a plurality of dual-energy attenuation images each havingdual-energy attenuation information representing the container and anoverlap region wherein the background object and the unknown object andcontainer overlap; decomposing each of the dual-energy attenuationimages into reference material equivalent path length images; removingthe reference material equivalent path lengths representing thebackground object from the reference material equivalent path lengthimages to provide reference material equivalent path lengthsrepresenting the unknown object and the container; converting thereference material equivalent path lengths representing the unknownobject into unknown object path lengths multiplied by a predeterminedscaling factor; determining the effective atomic number for each pixelrepresenting the unknown object and the container; determining the massthickness for each pixel representing the unknown object and thecontainer, the mass thickness being equivalent to the unknown objectpath lengths multiplied by the scaling factor; identifying each firstsource-detector pair line defined by a first x-ray extending between afirst one of the at least two sources and one detector of the array ofdetectors in a first one of the plurality of dual-energy attenuationimages on which lies one scaled unknown object path length; identifyingeach second source-detector pair line defined by a second x-rayextending between a second one of the at least two sources and onedetector of the array of detectors in a second one of the plurality ofdual-energy attenuation images on which lies one other scaled unknownobject path length, the second one of the plurality of dual-energyattenuation images generated contemporaneously with the first one of theplurality of dual-energy attenuation images; joining the extremities ofeach of the scaled unknown object path lengths to provide a contour ofthe unknown object; iteratively matching the contour of the unknownobject of each of the first and the second one of the plurality ofdual-energy attenuation images to reduce the scaling factor of thescaled unknown object path lengths and to provide unknown object pathlengths; defining the contour of the unknown object as an inner contourof the container; identifying third source-detector pair lines definedby third x-rays extending between each source and one detector of thearray which intersect with the container at only one point ofintersection in each of the first and second one of the plurality ofdual-energy attenuation images and delimit an outer bound of thecontainer as the pixels within the third source-detector lines;interpolating the outer bound of the container extending between the onepoint of intersection of each third source-detector pair line to definean outer contour of the container; determining path lengths representingthe container as path lengths which extend between the inner contour ofthe container and the outer contour of the container; and, determining adensity of the unknown object and an effective atomic number of theunknown object.
 2. The method according to claim 1, wherein the step ofdecomposing the plurality of dual-energy attenuation images intoreference material equivalent path length images further comprises thesteps of: scanning in the x-ray scanning device, first and secondreference materials each having known atomic composition, knowndimensions and known orientation in the x-ray scanning device, the x-rayscanning device emitting x-rays which pass through the first referencematerial with first reference material path lengths and through thesecond reference material with second reference material path lengths toprovide dual-energy x-ray attenuation information; associating thedual-energy x-ray attenuation information for each pixel in thedual-energy attenuation images with each of the first reference materialpath lengths and the second reference material path lengths; expressingcollectively each of the first reference material equivalent pathlengths and the second reference material equivalent path lengths as afunction of the associated dual-energy x-ray attenuation information todefine dual-energy attenuation surfaces; and, imposing dual-energyattenuation information of the dual-energy attenuation images onto thedual-energy attenuation surfaces to determine corresponding firstreference material equivalent path lengths and second reference materialequivalent path lengths corresponding with the dual-energy attenuationinformation.
 3. The method according to claim 1, wherein the step ofdecomposing the plurality of dual-energy attenuation images intoreference material equivalent path length images further comprises thesteps of: retrieving from lookup tables saved dual-reference materialequivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the dual-energy attenuationimages.
 4. The method according to claim 1 wherein dual-energyattenuation images include low-energy attenuation images and high-energyattenuation images, the dual-reference material equivalent path lengthimages include first reference material equivalent path length imagesand second reference material equivalent path length images and thedual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information. 5.The method according to claim 2, wherein the expressing step furthercomprises: selecting a model for expressing collectively each of thefirst reference material equivalent path lengths and the secondreference material equivalent path lengths as a function of theassociated dual-energy x-ray attenuation information to definedual-energy attenuation surfaces.
 6. The method according to claim 2,wherein the expressing step further comprises the step of: invertingnumerically point-by-point the dual-energy attenuation surfaces using anoptimization algorithm to provide inverse dual-energy attenuationsurfaces.
 7. The method according to claim 5, wherein the model is asecond model, the dual-energy attenuation surfaces are inverseattenuation surfaces, and prior to the associating step, the methodfurther comprises the steps of: associating each of the dual-energyx-ray attenuation information with corresponding ones of each of thefirst reference material equivalent path lengths and the secondreference material equivalent path lengths; and, selecting a first modelfor expressing collectively the dual-energy x-ray attenuationinformation as a function of the first reference material equivalentpath lengths and the second reference material equivalent path lengthsto define direct attenuation surfaces.
 8. The method according to claim5, wherein the step of selecting the model further includes the stepsof: selecting a set of coefficients to be applied to the model forfitting the dual-energy x-ray attenuation information with the model;and, fitting the dual-energy x-ray attenuation information with themodel by optimizing the coefficients.
 9. The method according to claim5, wherein the step of selecting the model further includes the stepsof: selecting the set of fitting constraints to be applied to the modelfor selecting the coefficients; and, selecting the set of coefficientsby applying the set of fitting constraints to the model.
 10. The methodaccording to claim 7, wherein the step of selecting the first modelfurther includes the steps of: selecting a first set of coefficients tobe applied to the first model for fitting the dual-energy x-rayattenuation information with the first model; and, fitting thedual-energy x-ray attenuation information with the first model byoptimizing the first coefficients; and, the step of selecting the secondmodel further includes the steps of: selecting a second set ofcoefficients to be applied to the second model for fitting thedual-energy x-ray attenuation information with the second model; and,fitting the dual-energy x-ray attenuation information with the secondmodel optimizing the second set of coefficients.
 11. The methodaccording to claim 10, wherein the step of selecting the first modelfurther includes the steps of: selecting a first set of fittingconstraints to be applied to the first model for selecting the first setof coefficients; and, selecting the set of first coefficients byapplying the first set of fitting constraints to the first model; and,the step of selecting second the model further includes the steps of:selecting a second set of fitting constraints to be applied to thesecond model for selecting the second set of coefficients; and,selecting the second set of coefficients by applying the second set offitting constraints to the second model.
 12. The method according toclaim 5, wherein the dual-energy x-ray attenuation information includeshigh-energy x-ray attenuation information and low-energy x-rayattenuation information, and wherein the associating step furthercomprises: defining a first space wherein the low-energy x-rayattenuation information of the first reference material and the secondreference material defines a first plane and first reference materialequivalent path lengths and second reference material equivalent pathlengths each define a first height over the first plane; defining asecond space wherein the high-energy x-ray attenuation information ofthe first reference material and the second reference material defines asecond plane and first reference material equivalent path lengths andsecond reference material equivalent path lengths each define a secondheight over second the plane; and, representing collectively the firstreference material equivalent path lengths and the second referencematerial equivalent path lengths using the model to define thedual-energy attenuation surfaces.
 13. The method according to claim 7,wherein the dual-energy x-ray attenuation information includeshigh-energy x-ray attenuation information and low-energy x-rayattenuation information wherein the associating step further comprises:defining a space wherein the first reference material equivalent pathlengths and the second reference material equivalent path lengths definea first plane and the high-energy x-ray attenuation information and thelow-energy x-ray attenuation information each define a respective firstand second height over the first plane and represent collectively thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information using the first model to define the directattenuation surfaces; and, defining an inverse space wherein thelow-energy x-ray attenuation information and the high-energy x-rayattenuation information define a second plane and first referencematerial equivalent path lengths and second reference materialequivalent path lengths each define a respective third and fourth heightover the second plane and representing collectively the first referencematerial equivalent path lengths and the second reference materialequivalent path lengths using the second model to define the inverseattenuation surfaces.
 14. The method according to claim 2, furthercomprising the steps of: determining the mass density of each of thefirst and second reference materials; determining a product of the firstreference material equivalent path lengths and the mass density of thefirst reference material to provide a first reference material massthickness; determining a product of the second reference materialequivalent path lengths and the mass density of the second referencematerial to provide a second reference material mass thickness; and,determining a total reference material mass thickness by summing thefirst reference material mass thickness and the second referencematerial mass thickness.
 15. The method according to claim 14, whereinthe dual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information,and wherein the step of decomposing each of the dual-energy attenuationimages into reference material equivalent path length images furthercomprises the steps of, for each of the first and second referencematerials: determining an energy-dependent attenuation cross sectionbased on each of the high-energy x-ray attenuation information and thelow-energy x-ray attenuation information; defining a Z_(eff)-dependentcross-section wherein a Z_(eff) value is dependent on each of thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information; evaluating an energy-dependent materialtransmittance function using each of the energy-dependent attenuationcross sections; re-evaluating the energy-dependent materialtransmittance function using each of the Z_(eff)-dependentcross-sections to provide a high-energy level domain Z_(eff)-dependentmaterial transmittance function, a high-energy level domain weightedsquared transmission error, a low-energy level domain Z_(eff)-dependentmaterial transmittance function, and a low-energy level domain weightedsquared transmission error; and, minimizing the low-energy level domainweighted squared transmission error to assign a Z_(eff) value to each ofthe first and second reference materials.
 16. The method according toclaim 15, wherein the step of determining the energy-dependentattenuation cross section based on each of the low-energy x-rayattenuation information and the high-energy x-ray attenuationinformation further comprises the step of, for each of the first andsecond reference materials: determining one of an average, a median anda mean of energy-dependent attenuation cross-sections per mol ofelectron of each element in the reference material, weighted by thetotal number of electrons of each element in the reference material. 17.The method according to claim 16 wherein the step of determining the oneof the average, the median and the mean of energy-dependent attenuationcross-section per mol of electron of each element in the referencematerial further comprises the steps of, for each of the first andsecond reference material: determining the product of a known massattenuation coefficient of the reference material and a molar mass overthe number of electrons per unionized atom of each element in thereference material.
 18. The method according to claim 15, wherein thestep of defining Z_(eff)-dependent cross-section further comprises thestep of, for each of the first and second reference materials:determining a linear combination of energy-dependent attenuationcross-sections of each of the two elements having atomic numbersimmediately adjacent to the effective atomic number value on which theZ_(eff)-dependent cross-section is based.
 19. The method according toclaim 16, wherein the step of evaluating an energy-dependent materialtransmittance function further comprises, for each of the first andsecond reference materials: evaluating an inverse exponential functionof an electron density of the reference material and theenergy-dependent attenuation cross-section of the reference material.20. The method according to claim 15, wherein the step of minimizing thelow-energy level domain weighted squared transmission error furthercomprises the step of, for each of the first and second referencematerials: integrating a weighted difference between theenergy-dependent material transmittance function and the correspondingZ_(eff)-dependent material transmittance function.
 21. The methodaccording to claim 1, wherein the step of converting the referencematerial equivalent path lengths representing the unknown object intounknown object path lengths multiplied by a predetermined scaling factorfurther comprises the step of: applying the following function for eachof the first and second reference material equivalent path lengthsrepresenting the unknown object: $\begin{matrix}{{{t_{o}\left( {i,j} \right)} = {\frac{\rho \; {t_{ob}\left( {i,j} \right)}}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}}\begin{matrix}{{t_{o}^{*}\left( {i,j} \right)} = {\rho \; {t_{ob}\left( {i,j} \right)}\left( {{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right) \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {SF}}}\end{matrix}} & \; \\{{{With}\mspace{14mu} {SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}\mspace{14mu} {when}\mspace{14mu} {t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}} & \;\end{matrix}$ wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants.22. The method according to claim 1, wherein the dual-energy attenuationinformation includes high-energy attenuation information and low-energyattenuation information and wherein the step of determining theeffective atomic number of the unknown object further comprises thesteps of: determining a first weight fraction of each of the first andsecond reference materials in the unknown object; determining a secondweight fraction of each element of each of the first and secondreference materials in the unknown object; determining a massattenuation coefficient of the unknown object; determining anenergy-dependent attenuation cross section of the unknown object;defining a Z_(eff)-dependent cross-section of the unknown object whereina Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation; evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections;re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror; and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to the unknown object. 23.The method according to claim 22, wherein the step of determining themass attenuation coefficient for the unknown object further comprisesthe step of: determining an effective weight fraction of each element ofeach reference material in the unknown material; determining a massattenuation coefficient of each element of each reference material inthe unknown material; and, determining a product of the effective weightfraction and mass attenuation coefficient of each element of eachreference material in the unknown material.
 24. The method according toclaim 1, wherein the background object is a predetermined backgroundobject, and wherein the step of removing the reference materialequivalent path lengths representing the background object from thereference material equivalent path length images further comprises thesteps of: scanning the predetermined background object in a plurality ofpositions and orientations within an x-ray scanning device to obtain aplurality of predetermined background object dual-energy attenuationimages each having predetermined background object dual-energyattenuation information representing the predetermined backgroundobject; decomposing the predetermined background object dual-energyattenuation images into predetermined background object dual-referencematerial equivalent path length images having predetermined backgroundobject reference material equivalent path lengths passing through thepredetermined background object; determining the position andorientation of the background object in one of the background objectdual-energy attenuation images and the dual-reference materialequivalent path length images of the unknown object by using asegmentation algorithm to localize the background object; determining,by comparison, corresponding ones of the plurality of predeterminedbackground object reference material equivalent path length images whichmost closely corresponds with the position and orientation of thebackground object in the dual-reference material equivalent path lengthimages; and, eliminating the predetermined background object referencematerial equivalent path lengths of the corresponding ones of theplurality of the predetermined background object reference materialequivalent path length images from the overlap region in thedual-reference material equivalent path length images of the unknownobject to provide reference material equivalent path length imageshaving first and second reference material equivalent path lengthspassing through only the unknown object.
 25. The method according toclaim 1, wherein the background object is unknown and has a homogenouscomposition and thickness, wherein the dual-energy attenuation imagesrepresenting the unknown object include pixels distributed in rows andcolumns and having dual-energy attenuation information, and whereindual-reference material equivalent path length images of the unknownobject include a background region with first and second referencematerial equivalent path lengths passing through only the backgroundobject and an overlap region with first and second reference materialequivalent path lengths passing through the unknown object overlappingwith the background object, the step of removing the reference materialequivalent path lengths representing the background object from thereference material equivalent path length images further comprising thesteps of: determining the background region and the overlap region byusing a segmentation algorithm to localize the background region;determining one of an average, a median and a mean of the first andsecond reference material equivalent path lengths passing through onlythe background object in each column; and, eliminating the one of theaverage, the median and the mean of the first and second referencematerial equivalent path lengths passing through only the backgroundobject from the first and second reference material equivalent pathlengths of each column of the overlap region to determine first andsecond reference material equivalent path lengths representing only theunknown object.
 26. The method according to claim 1, wherein thebackground object is unknown and has a homogenous composition, whereinthe dual-energy attenuation images representing the unknown objectinclude pixels distributed in columns and rows and having dual-energyattenuation information, and wherein the dual-reference materialequivalent path length images of the unknown object include a backgroundregion with first and second reference material equivalent path lengthspassing through the background object and an overlap region with firstand second reference material equivalent path lengths passing throughthe unknown object overlapping with the background object, the step ofremoving the reference material equivalent path lengths representing thebackground object from the reference material equivalent path lengthimages further comprising the steps of: obtaining a three-dimensionalmodel of the background object according to the position and orientationof the background object as scanned in the x-ray scanning device;determining first and second reference material equivalent path lengthsthrough the background object in the three-dimensional model for eachpixel using a ray casting algorithm; determining the effective atomicnumber of each pixel in the dual-reference material path length imagesof the background object; determining the density of each pixel in thedual-reference material path length images of the background object;determining the mass thickness of the background object by multiplyingthe determined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject; localizing the background region and the overlap region in thedual-reference material path length images by using a segmentationalgorithm; eliminating the mass thickness of the background object fromthe mass thickness of the reference material path length images toobtain a mass thickness of the unknown object; and, determining thefirst and second reference material equivalent path lengths through theunknown object.
 27. The method according to claim 1, wherein the step ofdetermining the effective atomic number of the container furtherincludes the steps of: identifying a pixel which has traversed only awall of the container; and, determining the effective atomic numberassociated with the attenuation information of the identified pixel asprovided by the step of decomposing each of the dual-energy attenuationimages into dual-reference material equivalent path length images. 28.The method according to claim 1, wherein the step of determiningcontainer path lengths representing the container further comprises thesteps of: extending at least one of the first and second source-detectorpair lines passing through the object of interest from the inner contourof the container to the outer contour of the container using a raycasting algorithm; subtracting the extended at least one of the firstand second source-detector pair lines from the corresponding at leastone of the first and second source-detector pair lines to provide atleast one of first and second source-detector pair line segments; and,determining a path length of the at least one of first and secondsource-detector pair line segments.
 29. The method according to claim 1,wherein the background object is a security screening tray, and afterthe step of interpolating the outer bound of the container to define theouter contour of the container, the method further comprises the stepsof: detecting the presence of an empty space within the container;determining points of intersection representing a first interfacebetween the object of interest and the empty space from points ofintersection representing a second interface between the unknown objectand the container; reflecting the points representing the firstinterface and the points representing the container wall relative to anaxis that is parallel to a surface of the tray; eliminating points underthe axis; and, joining sections of the container contour usinginterpolation.
 30. The method according to claim 1, further comprisingthe steps of: evaluating a periodicity of one of a container wallthickness and a radial size of the unknown object; and, if theperiodicity is regular, applying the periodicity to the one of thecontainer wall thickness and the radial size of the unknown object todetermine the container wall thickness.
 31. The method according toclaim 1, wherein the step of determining the effective atomic number ofthe unknown object further comprises the steps of: for path lengths on asupporting line passing through the unknown object and the backgroundobject, solving individuallyρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k) for pairs of path lengths where o represents the object ofinterest, b represents the background, ob represents the overlap region,pixels are represented by i, slices by j and views by k.
 32. The methodaccording to claim 1, wherein the step of determining the effectiveatomic number of the unknown object further comprises the steps of:fitting linearly on the following equations:$\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$with the regressor $\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$ and thepredictor $\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}}$$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$with the regressor $\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$ and thepredictor$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$wherein, the slope of the first equation is ρ_(o) and the slope of thesecond equation is g[Z_(o)]ρ_(o), and the intersection in the firstequation gives ρ_(b).
 33. The method according to claim 1, wherein thestep of determining the effective atomic number of the unknown objectfurther comprises the steps of: fitting on the following bivariatelinear functions:ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k) with theregressors t_(o) (i,j,k) and t_(b) (i,j,k), and the predictorρt_(ob)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k) with the regressors t_(o) (i,j,k) and t_(b)(i,j,k) and the predictor g[Z_(ob)(i,j,k)]ρt_(ob) (i,j,k) wherein, forthe first equation, the slope in direction x at y=0 is ρ_(o) and theslope in direction y at x=0 is ρ_(b), for the second equation, the slopein direction x at y=0 is g[Z_(o)]ρ_(o) and the slope in direction y atx=0 is g[Z_(b)]ρ_(b), and; obtaining g[Z_(o)] can be by dividingg[Z_(o)]ρ_(o) by the previously obtained ρ_(o), and Z_(o) obtained withg⁻¹{g[Z_(o)]}.
 34. A method for assigning attributes to an unknownobject comprising: scanning the unknown object at least partiallyoverlapping with a background object within an x-ray scanning device,the x-ray scanning device emitting x-rays from at least two sourceswhich pass through the object of interest and the background object, thex-rays being detected by at least one array of detectors to provide aplurality of dual-energy attenuation images each having dual-energyattenuation information representing an overlap region wherein thebackground object and the unknown object overlap; decomposing each ofthe dual-energy attenuation images into reference material equivalentpath length images; removing the reference material equivalent pathlengths representing the background object from the reference materialequivalent path length images to provide reference material equivalentpath lengths representing the unknown object; converting the referencematerial equivalent path lengths representing the unknown object intounknown object path lengths multiplied by a predetermined scalingfactor; determining the mass thickness for each pixel representing theunknown object, the mass thickness being equivalent to the unknownobject path lengths multiplied by the scaling factor; identifying eachfirst source-detector pair line defined by a first x-ray extendingbetween a first one of the at least two sources and one detector of thearray of detectors in a first one of the plurality of dual-energyattenuation images on which lies one scaled unknown object path length;identifying each second source-detector pair line defined by a secondx-ray extending between a second one of the at least two sources and onedetector of the array of detectors in a second one of the plurality ofdual-energy attenuation images on which lies one other scaled unknownobject path length, the second one of the plurality of dual-energyattenuation images generated contemporaneously with the first one of theplurality of dual-energy attenuation images; joining the extremities ofeach of the scaled unknown object path lengths to provide a contour ofthe unknown object; iteratively matching the contour of the unknownobject of each of the first and the second one of the plurality ofdual-energy attenuation images to reduce the scaling factor of theunknown object path lengths and to provide unknown object path lengths;and, determining a density of the unknown object and an effective atomicnumber of the unknown object.
 35. The method according to claim 34,wherein the step of decomposing the plurality of dual-energy attenuationimages into reference material equivalent path length images furthercomprises the steps of: scanning in the x-ray scanning device, first andsecond reference materials each having known atomic composition, knowndimensions and known orientation in the x-ray scanning device, the x-rayscanning device emitting x-rays which pass through the first referencematerial with first reference material path lengths and through thesecond reference material with second reference material path lengths toprovide dual-energy x-ray attenuation information; associating thedual-energy x-ray attenuation information for each pixel in thedual-energy attenuation images with each of the first reference materialpath lengths and the second reference material path lengths; expressingcollectively each of the first reference material equivalent pathlengths and the second reference material equivalent path lengths as afunction of the associated dual-energy x-ray attenuation information todefine dual-energy attenuation surfaces; and, imposing dual-energyattenuation information of the dual-energy images onto the dual-energyattenuation surfaces to determine corresponding first reference materialequivalent path lengths and second reference material equivalent pathlengths corresponding with the dual-energy attenuation information. 36.The method according to claim 34, wherein the step of decomposing theplurality of dual-energy attenuation images into reference materialequivalent path length images further comprises the steps of: retrievingfrom lookup tables saved dual-reference material equivalent path lengthsassociated with the dual-energy x-ray attenuation informationcorresponding with the dual-energy attenuation images.
 37. The methodaccording to claim 35 wherein dual-energy attenuation images includelow-energy attenuation images and high-energy attenuation images, thedual-reference material equivalent path length images include firstreference material equivalent path length images and second referencematerial equivalent path length images and the dual-energy x-rayattenuation information includes high-energy x-ray attenuationinformation and low-energy x-ray attenuation information.
 38. The methodaccording to claim 35, wherein the expressing step further comprises:selecting a model for expressing collectively each of the firstreference material equivalent path lengths and the second referencematerial equivalent path lengths as a function of the associateddual-energy x-ray attenuation information to define dual-energyattenuation surfaces.
 39. The method according to claim 35, wherein theexpressing step further comprises the step of: inverting numericallypoint-by-point the dual-energy attenuation surfaces using anoptimization algorithm to provide inverse dual-energy attenuationsurfaces.
 40. The method according to claim 38, wherein the model is asecond model, the dual-energy attenuation surfaces are inverseattenuation surfaces, and prior to the associating step, the methodfurther comprises the steps of: associating each of the dual-energyx-ray attenuation information with corresponding ones of each of thefirst reference material equivalent path lengths and the secondreference material equivalent path lengths; and, selecting a first modelfor expressing collectively the dual-energy x-ray attenuationinformation as a function of the first reference material equivalentpath lengths and the second reference material equivalent path lengthsto define direct attenuation surfaces.
 41. The method according to claim38, wherein the step of selecting the model further includes the stepsof: selecting a set of coefficients to be applied to the model forfitting the dual-energy x-ray attenuation information with the model;and, fitting the dual-energy x-ray attenuation information with themodel by optimizing the coefficients.
 42. The method according to claim41, wherein the step of selecting the model further includes the stepsof: selecting the set of fitting constraints to be applied to the modelfor selecting the coefficients; and, selecting the set of coefficientsby applying the set of fitting constraints to the model.
 43. The methodaccording to claim 40, wherein the step of selecting the first modelfurther includes the steps of: selecting a first set of coefficients tobe applied to the first model for fitting the dual-energy x-rayattenuation information with the first model; and, fitting thedual-energy x-ray attenuation information with the first model byoptimizing the first coefficients; and, the step of selecting the secondmodel further includes the steps of: selecting a second set ofcoefficients to be applied to the second model for fitting thedual-energy x-ray attenuation information with the second model; and,fitting the dual-energy x-ray attenuation information with the secondmodel optimizing the second set of coefficients.
 44. The methodaccording to claim 43, wherein the step of selecting the first modelfurther includes the steps of: selecting a first set of fittingconstraints to be applied to the first model for selecting the first setof coefficients; and, selecting the set of first coefficients byapplying the first set of fitting constraints to the first model; and,the step of selecting second the model further includes the steps of:selecting a second set of fitting constraints to be applied to thesecond model for selecting the second set of coefficients; and,selecting the second set of coefficients by applying the second set offitting constraints to the second model.
 45. The method according toclaim 38, wherein the dual-energy x-ray attenuation information includeshigh-energy x-ray attenuation information and low-energy x-rayattenuation information, and wherein the associating step furthercomprises: defining a first space wherein the low-energy x-rayattenuation information of the first reference material and the secondreference material defines a first plane and first reference materialequivalent path lengths and second reference material equivalent pathlengths each define a first height over the first plane; defining asecond space wherein the high-energy x-ray attenuation information ofthe first reference material and the second reference material defines asecond plane and first reference material equivalent path lengths andsecond reference material equivalent path lengths each define a secondheight over second the plane; and, representing collectively the firstreference material equivalent path lengths and the second referencematerial equivalent path lengths using the model to define thedual-energy attenuation surfaces.
 46. The method according to claim 40,wherein the dual-energy x-ray attenuation information includeshigh-energy x-ray attenuation information and low-energy x-rayattenuation information and wherein the associating step furthercomprises: defining a space wherein the first reference materialequivalent path lengths and the second reference material equivalentpath lengths define a first plane and the high-energy x-ray attenuationinformation and the low-energy x-ray attenuation information each definea respective first and second height over the first plane and representcollectively the high-energy x-ray attenuation information and thelow-energy x-ray attenuation information using the first model to definethe direct attenuation surfaces; and, defining an inverse space whereinthe low-energy x-ray attenuation information and the high-energy x-rayattenuation information define a second plane and first referencematerial equivalent path lengths and second reference materialequivalent path lengths each define a respective third and fourth heightover the second plane and representing collectively the first referencematerial equivalent path lengths and the second reference materialequivalent path lengths using the second model to define the inverseattenuation surfaces.
 47. The method according to claim 35, furthercomprising the steps of: determining the mass density of each of thefirst and second reference materials; determining a product of the firstreference material equivalent path lengths and the mass density of thefirst reference material to provide a first reference material massthickness; determining a product of the second reference materialequivalent path lengths and the mass density of the second referencematerial to provide a second reference material mass thickness; and,determining a total reference material mass thickness by summing thefirst reference material mass thickness and the second referencematerial mass thickness.
 48. The method according to claim 47, whereinthe dual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information,and wherein the step of decomposing further comprises the steps of, foreach of the first and second reference materials: determining anenergy-dependent attenuation cross section based on each of thehigh-energy x-ray attenuation information and the low-energy x-rayattenuation information; defining a Z_(eff)-dependent cross-sectionwherein a Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation; evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections;re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror; and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to each of the first andsecond reference materials.
 49. The method according to claim 48,wherein the step of determining the energy-dependent attenuation crosssection based on each of the low-energy x-ray attenuation informationand the high-energy x-ray attenuation information further comprises thestep of, for each of the first and second reference materials:determining at least one of an average, a median and a mean ofenergy-dependent attenuation cross-sections per mol of electron of eachelement in the reference material, weighted by the total number ofelectrons of each element in the reference material.
 50. The methodaccording to claim 49 wherein the step of determining the one of theaverage, the median and the mean energy-dependent attenuationcross-section per mol of electron of each element in the referencematerial further comprises the steps of, for each of the first andsecond reference material: determining the product of a known massattenuation coefficient of the reference material and a molar mass overthe number of electrons per unionized atom of each element in thereference material.
 51. The method according to claim 48, wherein thestep of defining Z_(eff)-dependent cross-section further comprises thestep of, for each of the first and second reference materials:determining a linear combination of energy-dependent attenuationcross-sections of each of the two elements having atomic numbersimmediately adjacent to the effective atomic number value on which theZ_(eff)-dependent cross-section is based.
 52. The method according toclaim 48, wherein the step of evaluating an energy-dependent materialtransmittance function further comprises, for each of the first andsecond reference materials: evaluating an inverse exponential functionof an electron density of the reference material and theenergy-dependent attenuation cross-section of the reference material.53. The method according to claim 48, wherein the step of minimizing thelow-energy level domain weighted squared transmission error furthercomprises the step of, for each of the first and second referencematerials: integrating a weighted difference between theenergy-dependent material transmittance function and the correspondingZ_(eff)-dependent material transmittance function.
 54. The methodaccording to claim 34, wherein the step of converting the referencematerial equivalent path lengths representing the unknown object intounknown object path lengths multiplied by a predetermined scaling factorfurther comprises the step of: applying the following function for eachof the first and second reference material equivalent path lengthsrepresenting the unknown object: $\begin{matrix}{{{t_{o}\left( {i,j} \right)} = {\frac{\rho \; {t_{ob}\left( {i,j} \right)}}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}}\begin{matrix}{{t_{o}^{*}\left( {i,j} \right)} = {\rho \; {t_{ob}\left( {i,j} \right)}\left( {{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right) \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {scaling}\mspace{14mu} {factor}}} \\{= {{t_{o}\left( {i,j} \right)} \times {SF}}}\end{matrix}} & \; \\{{{With}\mspace{14mu} {SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}\mspace{14mu} {when}\mspace{14mu} {t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}} & \;\end{matrix}$ wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants.55. The method according to claim 47, wherein the dual-energyattenuation information includes high-energy attenuation information andlow-energy attenuation information and wherein the step of determiningthe effective atomic number of the unknown object further comprises thesteps of: determining a first weight fraction of each of the first andsecond reference materials in the unknown object; determining a secondweight fraction of each element of each of the first and secondreference materials in the unknown object; determining a massattenuation coefficient of the unknown object; determining anenergy-dependent attenuation cross section of the unknown object;defining a Z_(eff)-dependent cross-section of the unknown object whereina Z_(eff) value is dependent on each of the high-energy x-rayattenuation information and the low-energy x-ray attenuationinformation; evaluating an energy-dependent material transmittancefunction using each of the energy-dependent attenuation cross sections;re-evaluating the energy-dependent material transmittance function usingeach of the Z_(eff)-dependent cross-sections to provide a high-energylevel domain Z_(eff)-dependent material transmittance function, ahigh-energy level domain weighted squared transmission error, alow-energy level domain Z_(eff)-dependent material transmittancefunction, and a low-energy level domain weighted squared transmissionerror; and, minimizing the low-energy level domain weighted squaredtransmission error to assign a Z_(eff) value to the unknown object. 56.The method according to claim 55, wherein the step of determining themass attenuation coefficient for the unknown object further comprisesthe step of: determining an effective weight fraction of each element ofeach reference material in the unknown material; determining a massattenuation coefficient of each element of each reference material inthe unknown material; and, determining a product of the effective weightfraction and mass attenuation coefficient of each element of eachreference material in the unknown material.
 57. The method according toclaim 34, wherein the background object is a predetermined backgroundobject, and wherein the step of removing the reference materialequivalent path lengths representing the background object from thereference material equivalent path length images further comprises thesteps of: scanning the predetermined background object in a plurality ofpositions and orientations within an x-ray scanning device to obtain aplurality of predetermined background object dual-energy attenuationimages each having predetermined background object dual-energyattenuation information representing the predetermined backgroundobject; decomposing the predetermined background object dual-energyattenuation images into predetermined background object dual-referencematerial equivalent path length images having predetermined backgroundobject reference material equivalent path lengths passing through thepredetermined background object; determining the position andorientation of the background object in one of the dual-energyattenuation images and the dual-reference material equivalent pathlength images of the unknown object by using a segmentation algorithm tolocalize the background object; determining, by comparison,corresponding ones of the plurality of predetermined background objectreference material equivalent path length images which most closelycorresponds with the position and orientation of the background objectin the dual-reference material equivalent path length images; and,eliminating the predetermined background object reference materialequivalent path lengths of the corresponding ones of the plurality ofthe predetermined background object reference material equivalent pathlength images from the overlap region in the dual-reference materialequivalent path length images of the unknown object to provide referencematerial equivalent path length images having first and second referencematerial equivalent path lengths passing through only the unknownobject.
 58. The method according to claim 34, wherein the backgroundobject is unknown and has a homogenous composition and thickness,wherein the dual-energy attenuation images representing the unknownobject include pixels distributed in rows and columns and havingdual-energy attenuation information, and wherein dual-reference materialequivalent path length images of the unknown object include a backgroundregion with first and second reference material equivalent path lengthspassing through only the background object and an overlap region withfirst and second reference material equivalent path lengths passingthrough the unknown object overlapping with the background object, thestep of removing the reference material equivalent path lengthsrepresenting the background object from the reference materialequivalent path length images further comprising the steps of:determining the background region and the overlap region by using asegmentation algorithm to localize the background region; determining amean of the first and second reference material equivalent path lengthspassing through only the background object in each column; and,eliminating the mean of the first and second reference materialequivalent path lengths passing through only the background object fromthe first and second reference material equivalent path lengths of eachcolumn of the overlap region to determine first and second referencematerial equivalent path lengths representing only the unknown object.59. The method according to claim 37, wherein the background object isunknown and has a homogenous composition, wherein the dual-energyattenuation images representing the unknown object include pixelsdistributed in columns and rows and having dual-energy attenuationinformation, and wherein the dual-reference material equivalent pathlength images of the unknown object include a background region withfirst and second reference material equivalent path lengths passingthrough the background object and an overlap region with first andsecond reference material equivalent path lengths passing through theunknown object overlapping with the background object, the step ofremoving the reference material equivalent path lengths representing thebackground object from the reference material equivalent path lengthimages further comprising the steps of: obtaining a three-dimensionalmodel of the background object according to the position and orientationof the background object as scanned in the x-ray scanning device;determining first and second reference material equivalent path lengthsthrough the background object in the three-dimensional model for eachpixel using a ray casting algorithm; determining the effective atomicnumber of each pixel of the dual-reference material path length imagesof the background object; determining the mass density of each pixel ofthe dual-reference material path length images of the background object;determining the mass thickness of the background object by multiplyingthe determined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject; localizing the background region and the overlap region in thedual-reference material path length images by using a segmentationalgorithm; eliminating the mass thickness of the background object fromthe mass thickness of the reference material path length images toobtain a mass thickness of the unknown object; and, determining thefirst and second reference material equivalent path lengths through theunknown object.
 60. The method according to claim 34, wherein the stepof determining the effective atomic number of the unknown object furthercomprises the steps of: for path lengths on a supporting line passingthrough the unknown object and the background object, solvingindividually:ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o) +g[Z _(b)]ρ_(b) t_(b)(i,j,k) for pairs of path lengths where o represents the object ofinterest, b represents the background, ob represents the overlap region,pixels are represented by i, slices by j and views by k.
 61. The methodaccording to claim 34, wherein the step of determining the effectiveatomic number of the unknown object further comprises the steps of:fitting linearly on the following equations:$\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$with the regressor $\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$ and thepredictor $\frac{\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}}$$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$with the regressor $\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$ and thepredictor$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho \; {t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$wherein, the slope of the first equation is ρ_(o) and the slope of thesecond equation is g[Z_(o)]ρ_(o), and the intersection in the firstequation gives ρ_(b).
 62. The method according to claim 34, wherein thestep of determining the effective atomic number of the unknown objectfurther comprises the steps of: fitting on the following bivariatelinear functions:ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k) with theregressors t_(o) (i,j,k) and t_(b) (i,j,k), and the predictorρt_(ob)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k) with the regressors t_(o) (i,j,k) and t_(b)(i,j,k) and the predictor g[Z_(ob)(i,j,k)]ρt_(ob)(i,j,k) wherein, forthe first equation, the slope in direction x at y=0 is ρ_(o) and theslope in direction y at x=0 is ρ_(b), for the second equation, the slopein direction x at y=0 is g[Z_(o)]ρ_(o) and the slope in direction y atx=0 is g[Z_(b)]ρ_(b), and; obtaining g[Z_(o)] can be by dividingg[Z_(o)]ρ_(o) by the previously obtained ρ_(o), and Z_(o) obtained withg⁻¹{g[Z_(o)]}.